Ajax announced the change - which comes following an agreement between the club's board, the mayor of Amsterdam and the alderman for sports and recreation in the city - on Tuesday.
Cruyff passed away in March 2016 following a battle with cancer.
He was part of the legendary Ajax side of the 1970s that won three European Cups, pioneering 'total football' with the Amsterdam club and Netherlands, who he helped reach the World Cup final in 1974.
Cruyff later coached Ajax and led them to UEFA Cup Winners' Cup glory in 1987, though it was at Barcelona where he enjoyed his greatest success as a boss, winning the Spanish title four times while guiding the Catalans to a maiden European Cup triumph.
In a statement, Ajax said: "The parties are convinced that in this way justice is done to the memory of Johan Cruyff, and express the hope that the Johan Cruyff ArenA is an inspiration for players from all over the world."
Further to the stadium name change, the mayor and the alderman have also decided to name a street, square, bridge or other feature of the city of Amsterdam after Cruyff.
Ajax's announcement follows that of Barcelona, who revealed that their reserve team stadium would be renamed Estadi John Cruyff following the anniversary of his death last month.