Cruz made his proposal on his Facebook page, and his boyfriend accepted.
"I'd like to say, and share it with your friends, and with my friends: Do you want to marry me?" Cruz said on a video of about 2 minutes posted on the social media site on Wednesday. "It's an important step, it's a step I've thought about, it's a step that we have thought about."
Cruz also mentioned the proposal on his Twitter account, saying that he had taken an important step in his life and that he wants happiness for him and his partner as a couple.
Puerto Rican gay activist Pedro Julio Serrano, spokesman for the U.S.-based National Gay and Lesbian Task Force, said he will serve as the godfather at the couple's wedding.
The timing and location of the wedding was unknown. Same-sex marriage is not allowed in Puerto Rico, or in Florida, where Cruz has a home.
Cruz announced his sexual orientation in October, becoming what is believed to be the first pro boxer to come out as openly homosexual while still competing.
The boxer is a featherweight fighter and is 20-2-1 with 10 knockouts.