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.
