In 2005 Adams earned a BFA in musical theatre with a minor in dance from the Boston Conservatory of Music. In New York, he joined the international tour of the musical Chicago, later joining the Broadway cast. He was also in the original Broadway cast of The Pirate Queen. In 2007 he co-starred with Mario Lopez as Larry in the Broadway revival of A Chorus Line. In June 2009 he was in the original cast of the Broadway revival of Guys and Dolls.
In 2010, Adams played "Angelique" in the original Tony winning revival cast of La Cage Aux Folles on Broadway at the Longacre Theatre, starring Kelsey Grammer.
Adams originated and starred as Adam/Felicia in Priscilla, Queen of the Desert, which opened at the Palace Theater on March 20, 2011 after a short run in Toronto at the Princess of Wales Theatre.
In 2010, Adams, who is gay, was a part of a PSA for the It Gets Better campaign with cast members from Priscilla Queen of the Desert.
In 2011, Adams won two Broadway.com Audience Choice Awards, for "Favorite Breakthrough Performance" and "Favorite Diva Performance" for his role in Priscilla Queen of the Desert. Adams was also nominated for the 2011 Astaire Award for Best Dancer on Broadway and honored by the American Theatre Hall of Fame for his role in Priscilla, Queen of the Desert.
On February 4, 2014, Adams joined the first National Tour of Wicked and was the final actor to star in the role of Fiyero.
In 2016, Adams appeared in season 2 of the sketch LGBT-themed comedy web series Go-Go Boy Interrupted.
Other TV and Film credits include: Sex and the City 2, An Englishman in New York, "Smash," "As the World Turns," "Guiding Light," "Dancing with the Stars," "Rosie Live," "It Could Be Worse," "The Kennedy Center Honors," "Regis and Kelly," "Good Morning America," "The View," "The Macy's Thanksgiving Day Parade," "Best Time Ever with Neil Patrick Harris," and multiple telecasts of "The Tony Awards."
In July 2009, Adams and his boyfriend went to the Turtle Bay nightclub in Manhattan, where they were denied entry. The bouncer said that the white t-shirt that Adams was wearing did not meet the dress code. Adams reported that he and his boyfriend were holding hands, and the bouncer smirked at them when he refused them entry. Adams claims he then saw a group of men that he described as straight, some wearing white t-shirts, allowed into the bar. Adams posted the story to his blog, and Twitter, where his fans "went crazy". Eventually the manager of the bar posted an apology, and claimed it was a misunderstanding. Adams responded, "I was discriminated against. I will not give my business to Turtle Bay and I urge you to do the same. This womans [sic] attempt to brush this aside as a misunderstanding is disingenuous at best if not hurtful and offensive to myself and the gay community of New York City".