Johansson is the man who sent Sweden to the World Cup finals in Russia by scoring the winning goal in a play-off with Italy in November.
“Rennes are a very well structured club with fine training facilities and a great stadium,” Johansson told the Rennes website. “They also have a very clear and ambitious project.”
Rennes came fifth in Ligue 1 last season and are coached by former France midfielder Sabri Lamouchi.
Johansson was club captain at AEK in their title winning campaign but was omitted from Sweden's 23-man World Cup squad due to a knee injury that limited his appearances this season.
The 27-year-old has signed a two year deal at Rennes and moves on a free agent contract.