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 Ligue 1 outfit's website. "They also have a very clear and ambitious project."
Rennes came fifth in France's top division 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.
4 June 2018