The author and LGBT rights activist fell into the bottom two along with Hope Solo and her professional partner Maksim Chmerkovskiy when the judges' scores and viewer votes were combined.
Bono - who received a standing ovation from the judges - said: "I took so much away from this... this was an amazing journey that really pushed me and showed me that I could do so much more than I ever thought I could.
"I came on this show because I wanted to show America a different kind of man... if there was somebody like me on TV when I was growing up, my whole life would have been different."
Dedicating his achievements on Dancing with the Stars to "all the people out there like me, especially the kids and teens who are struggling", Bono added: "You can have a wonderful, great life and be successful and happy."
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Bono had scored 19 out of a possible 30 points for a tango which judge Bruno Tonioli felt lacked aggression. He was also seen backstage saying that he was hurt by Tonioli's description of him as "like... a cute penguin trying to be a big, menacing bird of prey".
Solo had scored 20 out of a possible 30 points for a rumba which Len Goodman said was her worst performance of the season so far, upsetting Chmerkovskiy and leading to a heated argument on Monday night's live show.
Chmerkovskiy also apologised for comments he made on Monday night's programme saying that Dancing with the Stars was 'his' show.
He explained: "I had an idea in my head and it came out wrong. It's not my show, I'm part of a very large cast and I'm very proud to be here. These guys are amazing, that's all."
Tonight's results show featured Broadway star Kristin Chenoweth performing 'Lessons Learned', the second single from her new album Some Lessons Learned. Country musician Martina McBride also sung 'I'm Gonna Love You Through It' from her recently-released album Eleven.
Former High School Musical star Corbin Bleu also performed with Macy's Stars of Dance in a Broadway tribute choreographed by Emmy award-winner Kenny Ortega.
Dancing with the Stars airs on Mondays and Tuesdays on ABC.