The five-round title bout will headline UFC 157 at Honda Center in Anaheim, Calif.
Rousey and Carmouche will become the first women mixed martial artists to compete in UFC.
UFC officials worked diligently to encourage former Strikeforce women's featherweight champion Cristiane "Cyborg" Santos to take the fight against Rousey at 135 pounds, but according to White, she refused.
Despite Santos' reluctance, White is confident the highly anticipated bout will eventually happen.
"That was obviously the fight (Rousey against Santos) we wanted to make at 135 pounds," White said. "We worked hard to make that fight.
"This fight (Rousey-Carmouche) will happen and I truly believe the next one will be the Cyborg fight -- this fight first, then Cyborg at 135 pounds.
"(Carmouche) wanted to fight her. Believe me, people aren't kicking the doors down at Zuffa to fight her."
Rousey signed a multifight deal with UFC in November, officially relinquishing her Strikeforce title.
She claimed the Strikeforce 135-pound title on March 3 with a first-round armbar submission of Miesha Tate.
The 2008 Olympic judo bronze-medal winner is 8-0 as a professional mixed martial artist. She has won all of her fights by armbar submission.
"I've got a lot of respect for Liz," Rousey said. "She's the only one who stepped up and said she wanted this fight right now."
Carmouche (7-2) has won two consecutive fights. Her bid for the Strikeforce bantamweight title was thwarted on March 5, 2011, when then-champion Marloes Coenen submitted her in the fourth round.
Santos is serving a year-long suspension after she tested positive for a banned substance following her featherweight title victory over Hiroko Yamanaka in December 2011.