The 22-year-old is moving to Amsterdam where he is expected to further his footballing education under manager Frank de Boer and assistant manager, and former Gunner, Dennis Bergkamp.
Sanogo joined Arsenal from Auxerre in July 2013 since when he has made a total of 20 appearances for his parent club, scoring once.
The Frenchman spent the second half of last season on loan at Crystal Palace for whom he played in 10 Premier League matches.
Sanogo has represented France at U21 level and Arsenal boss Arsene Wenger said of the loan move: “He needs to play.
“He came to us injured and it took us a while to get him to the top level. He’s ready to play now and I’m sure he can be a good signing for Ajax.
“He has an opportunity to play in the Champions League with Ajax, which is good experience. We have a good relationship with them and hopefully he can have a great season.”