In 1967, Velella graduated from St. John's University in Jamaica, New York. Velella then earned a law degree from the Suffolk School of Law (today the Suffolk University Law School) in Boston, Massachusetts. Velella joined his father's law practice.
In 1972, at the age of 28, Velella, a Republican, ran for the New York State Assembly in the East Bronx. The incumbent Democrat withdrew from the race unexpectedly, and Velella won the race easily. He served in the Assembly for 10 years. After redistricting, Velella found himself running in a new Democratic district in 1982. In a bitter campaign, he ran against Assemblyman John Dearie , a popular Democrat, and lost by a wide margin. Velella told the Bronx News, a local weekly newspaper, that he was done with politics. In January 1983, Velella returned to practicing law full-time.
Despite his pledge that his political career was over, Velella was elected to the local school board. Many observers expected Velella to run for the seat in Congress held by Mario Biaggi, a Democrat, when he retired.
Velella, however, returned to elected office on April 22, 1986, when he was elected to the New York State Senate in a special election to fill the unexpired term of State Senator John D. Calandra, who died on January 20, 1986. The three-way race was bitter and costly, as JoAnn Calandra, Calandra's widow, backed by the late senator's partisans and patronage recipients, and hoping to capitalize on the late senator’s ties to the Senate Majority establishment, sought to retain family control of the seat. The Democratic candidate, Michael Durso, also generated interest, and Velella's victory was anything but a sure bet. The seat, the 34th Senate District included mostly white neighborhoods in the Bronx and parts of lower Westchester County, areas hand-picked by Calandra during the last redistricting and including portions of Yonkers, Mount Vernon, New Rochelle and all of Pelham. Velella also received the endorsements of the Bronx Conservative Party, which is headed by Bill Newmark, and the now-defunct Right to Life Party.
In a battle that echoed those for the Republican nomination and the Senate Seat itself, Velella also became chairman of the Bronx Republican Party. He was subsequently re-elected to the State Senate in November 1986 and in every subsequent election. He resigned his seat on May 14, 2004 as part of a plea bargain reached on criminal charges that he took bribes to help businesses win lucrative state contracts. According to the text of the indictment, the bribes were in the form of payments to the Velellas' law firm for little or no work.
In 1989, Velella became chairman of the powerful Senate Insurance Committee. In this capacity, Velella secured passage of numerous laws affecting the insurance industry in New York.
Velella reached the height of his influence and power during the mid-1990s. He enjoyed access to important elected officials, many of them Republicans, such as U.S. Senator Alfonse D'Amato, Governor George Pataki, Attorney General Dennis Vacco, New York City Mayor Rudolph Giuliani, and NYS Senate Majority Leader Joseph Bruno. Velella used his many contacts to secure patronage jobs for his supporters. Other key backers such as Bill Newmark, the chairman of the Bronx Conservative Party, joined his legislative payroll. Velella's alliance with D'Amato was crucial and a central facet of Velella's power. During Rudy Giuliani's first mayoral bid in 1989, Velella and D'Amato acted together to deny Giuliani the support he needed to beat David Dinkins, the eventual Democratic nominee, even going so far as to engineer a completely spurious candidacy on the part of cosmetics heir Ronald Lauder to challenge Giuliani in the Republican primary. In fact, Victor B. Tosi, Velella's executive assistant and a long-time Bronx Republican activist, served as Lauder's campaign manager. Lauder lost the primary, but the nearly $13 million he spent on negative campaign commercials damaged Giuliani's candidacy. In the general election, Velella endorsed Giuliani, who went on to lose narrowly to Dinkins.
Later, when D'Amato and the Governor-Elect Pataki decided to foment a coup against then-Majority Leader Ralph Marino, with whom Pataki had repeatedly clashed during the governor’s brief tenure in the Senate, Velella acted as Pataki’s and D’Amato’s agent, drafting Senate Members for a Thanksgiving coup in 1994 against Marino and in favor of Rensselaerville County's Joe Bruno. This occurred even though Velella had been, upon the retirement of former Majority Leader Warren Anderson, one of a small circle who engineered the ascension of Long Island’s Marino to the Leader’s post, and was one of Marino’s most visible and rewarded allies during the ensuing years.
While serving in the state legislature, Velella also maintained a thriving law practice, which benefited from his Senate role as Insurance Chairman.He was a partner, with his father, in Velella, Velella, Basso, and Calandra, a law firm in Morris Park in the Bronx. After his conviction, Velella surrendered his law license and is no longer eligible to practice law. In 2004, the law firm changed its name to Velella, Basso, and Cirrincione.
In 1987, Velella admitted that he fathered a child out of wedlock with a woman in Albany whom he had a long-time affair. The year before, Velella's supporters distributed campaign literature that championed him as advocate of family values and criticized liberal Democrats for undermining sexual morality. Velella said he made financial arrangements with the mother to support his new child, Alexandra Velella.
In 1993, Velella was accused of fixing local school board elections. No criminal charges were filed.
A story, possibly attributed to Velella, states that he would never run for Mayor of New York because he did not want to be the answer to a trivia question: "Who was the man who ran for all three city-wide offices in New York City and lost?"
In 1986, Velella became the chairman of the Bronx Republican Party. He resigned that position in 2004. Critics charged that Velella did nothing to build the local GOP and maintained a "non-aggression pact" with the Bronx County Democratic organization. With the exception of himself, no other Republican was ever elected to any office in the Bronx during his 18-year term. In 1994 and 1996, Velella ran with the endorsement of the Bronx Democratic Party.
Although he maintained a cordial and mutually-beneficial relationship with the Bronx Democratic political machine, Velella did work hard to get Republicans elected to prominent offices. In 1992, Velella campaigned for Senator D'Amato, who was facing a tough re-election fight against Democratic challenger, New York Attorney General Robert Abrams. D'Amato was narrowly re-elected. Velella and Giuliani put aside their previous animosity, and the Bronx Republican leader enthusiastically campaigned for him in 1993. On Election Day, Velella oversaw a "ballot security program," which sought to deter voter fraud at the polls. In 1994, Velella devoted his resources to the Pataki and Vacco campaigns, which were both successful.
Starting in 1988, rumors that Velella was going to leave the State Senate were widely circulated in the district. It was thought that Velella was going to step down to spend more time with his family (which included a wife and four children) and possibly become a state or local judge. Although these rumors would be repeated in every election year, Velella always ran for re-election. Insiders alleged that Velella spread these false rumors himself in order to draw out whom he thought were disloyal subordinates who wanted to take his seat and undermine political opposition to him.
On June 21, 2004, Velella was sentenced to one year in jail for bribery under a plea deal, but was released from Rikers Island on September 28, 2004 after less than twelve weeks by the Local Conditional Release Commission, an obscure New York City agency. (In the State Senate, Velella had voted to abolish the Local Condition Release Commission.) Velella's early release sparked widespread outrage, especially in the media. Both the New York Post and the New York Daily News, which had both endorsed Velella in his past campaigns, published editorials demanding his return to jail. The New York Post even pasted Velella's face on a Monopoly "Get Out of Jail Free" card and published it daily in its opinion section.
Mayor Michael Bloomberg called for an investigation into the circumstances of Velella's early release. The city's Department of Investigations (DOI), which looked into the matter, found that the Local Conditional Release Commission violated established procedures when it granted Velella's request. On November 19, 2004, the commission ordered that Velella be returned to prison. Although Velella appealed this decision, the New York State Appeals Court refused to give him another reprieve.Velella returned to Rikers Island in late December to resume his sentence.
Velella was released on March 18, 2005, after serving only 182 days of his original one-year sentence.
Velella continues to receive an annual state pension of $80,000. In 2005, he told the New York Daily News that he does some political and business consulting. A year later, Velella was quoted as saying that he is planning to write a book that would embarrass many politicians, past and present. In 2007, Velella left the Bronx and purchased a new home in Eastchester, a town in Westchester County.