The bout will take place at UFC 157, with the winner possibly earning a 205-pound title shot.
Rousey-Carmouche represents the first women's bout in UFC history.
"Ronda is the real deal," UFC president Dana White said. "She's nasty. She's mean. She's like (retired former light heavyweight champion) Chuck Liddell. She goes out there and tries to finish her opponents.
"And Carmouche is tough as nails, too. She was a Marine and she's got great ground-and-pound. I look forward to having the women join the UFC."
Henderson (29-8) was slated to face light heavyweight Jon Jones on Sept. 1 at UFC 151 in Las Vegas. But an injury forced Henderson to withdraw from the bout.
Machida later rebuffed an offer from UFC officials to step in for Henderson.
The event was canceled after Jones refused to fight Henderson's eventual replacement, Chael Sonnen, on eight days' notice.
Henderson, on a four-fight win streak, has held 205-pound titles in Strikeforce and Pride. He also held the Pride 170-pound title belt.
Henderson has not fought since defeating Mauricio Rua by unanimous decision at UFC 139 in November 2011.
Machida, a former UFC light heavyweight champion, bounced back from a submission loss to Jones at UFC 140 with a second-round knockout of Ryan Bader on Aug. 4. He has a professional record of 18-3.