The two musicians began work on Spider-Man: Turn Off The Dark after Adams approached them in 2002 to write the score, but the production hit the buffers when Adams died of a stroke in 2005.
After a series of further setbacks, the show finally launched last year (11) to scathing reviews - but it ended 2011 on a high note, setting a new Broadway box office record for the highest single-week gross, taking more than ?1.8 million in post-Christmas sales.
In a statement, Bono says, "For all the problems, there was magic on the stage. Things did get chaotic and messy after our producer Tony Adams died. But this week's news has us all giddy again and we are raising our glasses to Tony, to our indefatigable cast, crew, creative and production team."
Guitarist The Edge adds, "It just goes to show that you can't keep a good superhero down. This is a proud day for everyone who has been a part of this show. The Broadway public have voted with their feet."