In 1983, his first TV role was in the 1983 TV movie For Love and Honor, but in 1984, his big role came when he played Napoleon "Napo" Rodriguez in the 1984 cult classic film Repo Man.
Eddie got his first TV series role in the soap opera Capitol in 1986 as Alonzo. He later on that year starred in the hit NBC TV series The A-Team as Frankie "Dishpan" Santana from 1986-1987 as a new member of the team. The show was in its 5th and final season. Eddie's other TV roles were in the series Trial and Error in 1988 as John Hernandez. He starred in True Blue as Officer Frankie Avila.
Eddie starred in the soap opera Port Charles and General Hospital as Det. Alexander Garcia, and later on starred in the soap opera Days of Our Lives as Paul Mendez.
Some of Eddie's other feature film roles were Doin' Time (1985), The Women's Club (1987), Rooftops (1989), Traffic (2000), White Chicks (2004) and his most recent film is Beautiful Loser in 2008.
Velez has made guest appearances on various programs, including Cagney & Lacey, Hill Street Blues, Walker, Texas Ranger, Pacific Blue, Charmed, and Numb3rs.