Joshua, 33, who lost back-to-back fights to world champion Oleksandr Usyk, will be seeking a first win since beating Kubrat Pulev in 2020.
BBC reports Franklin was beaten on points by Briton Dillian Whyte in November, marking a first loss in 22 fights for the 29-year-old American.
"I'm looking forward to stepping back into the ring," said Joshua.
"Mentally and physically I feel ready. I want to put on a show and impress my coach as he has high standards.
"Franklin has a good style and a great attitude, which he has shown in recent fights."
Joshua, a two-time world champion, lost by split decision as he sought to recapture the unified heavyweight titles from Usyk in August.
That was the Watford fighter's third career defeat in 27 bouts, following a shock loss to Andy Ruiz Jr in 2019 which he later avenged.
Franklin said: "I'm ready to show the world why it's time for me to take my place at the top of the heavyweight division.
"Joshua had his time. It's my time to shock the world."
Anthony Joshua lost his second bout against Oleksandr Usyk by split decision