The original song appears on Gaga's new album, Artpop, but features rapper R. Kelly. The "Applause" singer, 27, originally reached out to Aguilera, 33, to perform with her for The Voice season 5 finale.
"I was really excited because The Voice called and said they wanted me to perform on the finale, and I obviously can't refuse," Gaga told host Carson Daly following the Dec. 17 performance. "Such an amazing show! And I said I want to know if Christina wants to do it with me!"
The "Beautiful" singer responded, "When I heard she wanted to collaborate, I said of course! She's such an innovative artist and a risk taker. And as a fellow female, I have so much respect for that."
The two ladies were excited to surprise their fans and took to Twitter to announce the special single.
"Happy New Year! Loved performing #DWUW with @LadyGaga so we made a special version just in time for NYE! XoXtina," Aguilera tweeted.
"Happy New Years Twitterverse, I wish you a beautiful and happy 2014, I wanted to start little monsters 2014 with a surprise so...Here's 'Do What U Want feat. Christina Aguilera' STUDIO Version. pink champagne, gold lame, hair, and fearlessness," Gaga tweeted.
The two ladies were rumored to be in a feud around the start of Gaga's career in 2008, but before her Voice performance, the queen of the Little Monsters worked to dispel those rumors on a September appearance of Watch What Happens Live.
"I'm a very big fan of Christina Aguilera," she told Andy Cohen. "From the very beginning of when my career started there was all this controversy about the two of us, and I always felt that it was very unfair to her."