Barnes, 45, has been appointed manager of the League One outfit and will be assisted by former Liverpool team-mate and ex-Tranmere midfielder McAteer.
Johnson said: "I am delighted John has agreed to become our manager as he was our first choice for the position.
"With John and Jason as the club's management team they bring a wealth of experience, knowledge and contacts within the game.
"They are a Wirral-based partnership who are very enthusiastic about what they can offer Tranmere and I look forward to watching their team play next season.
"They have both had successful careers as players and hopefully they can be successful together in management at Tranmere."
Source: Team_Talk