Former IBF world light-heavyweight champion Johnson has lost 17 of his 51 fights, but his name-packed record includes victories over Roy Jones, Allan Green and Antonio Tarver.
The awkward 43-year-old Jamaican only lost to Carl Froch in the Super Six last year on a majority decision.
It will be Groves' 16th fight and the Commonwealth super-middleweight title holder knows it will be a challenging evening.
"I'm definitely ready for this fight for quite some time and it's the fight I've asked for," the 24-year-old said.
"Johnson is a good opponent who has been about and is a name. It's an early Christmas present for me and I can't wait.
"No one has an easy night against him and he's been rolling back the years, pushing Carl Froch.
"A good performance against him will definitely make people sit up and take notice of me. Then I'll be knocking on the door of a world title."
Groves will be fighting on the undercard of Ricky Burns' WBO lightweight title defence against an opponent expected to be announced on Thursday.