The singers were asked by U.S. Tv host Hoda Kotb to create the song for her Project Truly Brave campaign.
The track, which will debut on Thursday (25Sep14), will be a combination of Lauper's True Colors and Bareilles' Brave.
Bareilles tells U.S. breakfast show Today, "It's definitely been a tall order to mash these two songs up. Hopefully it just doesn't sound schizophrenic when we're done with it."
Lauper adds, "I hope you guys like it, pressure's on."