In , Burgos made his major league debut with the Kansas City Royals and appeared in 59 games as a relief pitcher. Despite pitching only 60 innings, he managed to be 10th in the league in wild pitches. In 2005, Burgos had the highest average fastball velocity of American League relievers, at 96.5 mph, and posted an ERA of 3.90.
In , Burgos started the season as the Royals' closer. However, the season was a disappointment as he finished with a 4-5 record and 5.52 ERA in 73 1/3 innings pitched. He had 18 saves, but also blew 12 saves and lost the closer's job midway through the season.
In , Burgos began the season on the Mets 25-man roster, but was sent to Triple-A soon thereafter. According to an Associated Press report on August 28, 2007, general manager Omar Minaya indicated that Burgos underwent Tommy John surgery and would be out for a prolonged period. On August 6, , Burgos pitched to nine batters in his first minor league rehab game.
On October 1, 2008, Burgos was indicted on charges of hit and run in his native Dominican Republic. Sources say that Burgos struck two women in his SUV and drove off. The women later died of their injuries. Burgos turned himself in to authorities on October 7.