The fight will be held at the Barclays Center on April 27, and Showtime will televise the event.
Mosley is one of the most accomplished boxers of his era, winning world titles in three different divisions. He was once considered one of the top pound-for-pound fighters in the world, and his career record is an impressive 46-8-1.
However, the 41-year-old hasn't fought since May 5, when he suffered a lopsided defeat at the hands of Saul "Canelo" Alvarez. Alvarez dominated Mosley throughout the fight, eventually winning by unanimous decision.
That was Mosley's second consecutive loss, and it pushed his record to 0-3-1 in his last four fights.
He hasn't won since 2009, and since then he has lost to Floyd Mayweather Jr. and Manny Pacquiao. Mosley was heavily out-pointed in both fights.
The best Mosley has looked in recent years was a split decision draw against Sergio Mora in September, 2010. He will have to improve on his past few performances in order to beat Malignaggi, who is 32-4 in his career.
Rafael also reported that Mosley will be trained once again by his father, Jack Mosley, who was named the Boxing Writer's Association of America's trainer of the year in 1998.
"I'm excited to have my father back with me as my coach," Mosley said. "To be able to go into a fight and (try to) win a world title again with my father in the corner, that is like a storybook. To go into a fight like this and have family in the corner and win another belt, it's going to be a great feeling."
The last time Jack Mosley was in his son's corner was in 2008.