The vastly experienced Johnson, 59, has been appointed until the end of the season, with Milton to be kept on as his assistant.
Cheltenham slumped to the foot of the League Two table on Saturday courtesy of a 3-0 home defeat to Plymouth Argyle and are two points from safety with seven matches to play.
Johnson, who becomes the club's fourth manager of the season, said: "I will be doing my best along with Russell to keep the club in the Football League.
"It's all hands on deck for the last seven games."
Arsenal report: Incredible Roberto Firmino deal 'close', following recent Mikel Arteta 'hint'
'Did I say no to Liverpool last summer? Yes, I did. But I'll be very clear: if this offer had come at the end of August, just before the end of the transfer window, I would have accepted it' Reds target admits he turned down Arne Slot's project
