Jesse was born in Virginia's Blue Ridge mountain range. His mother, Virginia Price, was a college career counselor. His father, Jesse Reed Watkins, was a truck driver. His parents divorced when he was very young. His mother then moved his family to Buffalo, New York. He and his four brothers took the surname of his mother's second husband. His family calls him by his middle name, Lamont. As a fourth-grader, a teacher cast him in a play and he found his passion. After graduating from high school, he worked in restaurants to afford the tuition at New York University. He then got work on soaps and did commercials. His breakthrough came in a role in Jonathan Larson's Pulitzer Prize-winning Broadway musical Rent. That was followed up with TV exposure in his first starring role in the series 413 Hope St., which aired on Fox.
He is a graduate of one of the United States' most famous academic art schools, the Buffalo Academy For Visual and Preforming Arts for grades 5-12 Is on the Board of Trustees for the Jonathan Larson Performing Arts Foundation Along with Jerry Orbach, Fred Dalton Thompson and Leslie Hendrix, he is one of only four actors to play the same character (Detective Ed Green) on all four "Law & Order" series (Law & Order, Law & Order: Special Victims Unit, Law & Order: Criminal Intent, and Law & Order: Trial by Jury). Has appeared in episodes of three different television series with Sam Waterston: Law & Order, Law & Order: Special Victims Unit and Law & Order: Trial by Jury. Performed the song "Razzle Dazzle" from the musical Chicago at the 2005 Tony Awards just as the "In Memoriam" section of the show was finishing. The last photo shown during the memorial was that of Jerry Orbach, who was both Martin's costar on Law and Order and the first person to perform "Razzle Dazzle" in the original Broadway production of Chicago. Appeared in episodes of three different series with Jerry Orbach: Law & Order, Law & Order: Special Victims Unit and Law & Order: Criminal Intent. Accompanied Jerry Orbach's widow Elaine to the 2005 Tony Awards. Worked at the Moondance Diner in New York City with Jonathan Larson. Almost Graduated from NYU Currently preparing two one-man shows: "Fiend" and an untitled piece based on the life of Marvin Gaye. In Law & Order, he works with Jerry Orbach, who played Billy Flynn in the original cast of Chicago. In Rent, (play and film) he works with Taye Diggs, who played the band leader in the 2002 film, and briefly played Flynn himself in late 2002 during the Broadway revival. Tom Collins and Angel Dumott Schunard, his character and character's boyfriend in Rent, take their last names from their characters counterparts in La Boheme. Tom Collins (known simply as Collins) is based on Colline, and Angel is based on Schaunard. On April 2, 2006, Martin was a featured guest at the awards ceremony of the SunDeis Film Festival at Brandeis University. Martin, introduced to a standing ovation, presented his "Law and Order" co-star S. Epatha Merkerson with the first-ever SunDeis Entertainer of the Year Award, the highlight of the festival weekend. The storyline of Detective Green being shot in the line of duty was written into the Law and Order script so that during his 'recovery', Jesse could be in San Fransisco to film Rent. Returning back to Buffalo, N.Y., working on an independent film, on October of 2006, his luggage was stolen from his car at the Buffalo International Airport. They still have not been returned.