The Toronto-born Elliott was drawn to acting after reading "King Lear" in a theater history class at age 19. He garnered positive notices as a member of Ontario's Stratford Shakespeare Festival before segueing to Canadian TV where he enjoyed a healthy run as the star of "Street Legal" (CBC, 1985-88). Signed by Disney to a development deal in 1990, Elliott moved to Los Angeles and began doing TV guest spots. He gained notice playing a furniture mover who dates Julia Louis-Dreyfus on "Seinfeld". Elliott was also memorable in a "Melrose Place" storyline as a sex-addicted recovering alcoholic who becomes involved with Courtney Thorne-Smith.

All of these roles were warm-ups for the role that would make him famous: the Naval legal eagle Harmon 'Harm' Rabb, Jr., the straight-laced All-American star (though the actor himself is Canadian) of the drama "JAG." As a former pilot grounded by night blindness who invesitgates and prosecutes crimes involving Naval and Marine personnel, Elliott was an easy fit for the Harm character in the series described by many as "Law & Order" meets "Top Gun." Despite Elliott's appeal in the lead role, NBC axed the series after just one 21-episode season in 1996, but the then-struggling CBS realized the show was a potentially good fit for its specific demographic and picked it up for a second season. The gamble paid off, and "JAG" quickly become one of the Eye network's most dependable ratings performers, particularly when the series was tweaked to make Harm a more well-rounded character and he was paired with a new partner (Catherine Bell) that stoked a subtext of sexual chemistry. With Elliott appealing to both men and women and series gradually developing its own engrossing mythology, it attracted a large and loyal audience that kept it on the air for several years. The series did particularly well in the immediate post-9/11 era, when support and interest in military matters were at an all-time high, and the series incorporated America's war on terrorism into its storylines. Finally, once Elliott announced his intention to leave the show following the 2004-2005 season and inked a development deal with ABC, the show cut back his screen time to experiment with a new character but the network ultimately pulled the plug on the series after ten seasons and 227 episodes.

The actor became a fixture of People's sexy celebrity lists and parlayed his "JAG" popularity into other roles, including the telepics "Dodson's Journey" (1996) and "Code 11-14" (2003), and he appeared in the occasional feature film, including "Clockwatchers" (1997) and "The Shrink Is In" (2001).