The fight at the 02 Arena will be the first time in nearly seven years that Joshua has fought without a world title at stake.
The Briton has not fought since his second straight loss to Ukraine's WBA, WBO, IBF and IBO champion Oleksandr Usyk (36) in a title rematch in Saudi Arabia last August.
"Mentally and physically I feel ready," said Joshua, who has a new trainer in Derrick James for the fight against his opponent.
Franklin, who has a 21-1 record with 14 knockouts and whose first defeat was on points to Britain's Dillian Whyte (34) at Wembley Arena last November, said Joshua had "had his time".