United had earlier confirmed that terms of the transfer had been agreed with the Dutch giants.
Blind, who left Ajax to move to Old Trafford in 2014 after impressing at that summer's World Cup, has now signed a four-year contract with his boyhood club that will run until 2022.
The 28-year-old played 141 games in all competitions during his four seasons with United, including 56 times during 2015/16 alone when Louis van Gaal used him as a centre-back.
Blind won FA Cup, EFL Cup and Europa League honours with United.
The player, whose father Danny captained Ajax to Champions League glory in 1995, first joined the youth ranks of the Amsterdam club at the age of eight. He made his first team debut in 2008 while still a teenager and won four Eredivisie titles during his first spell.
Blind was named Dutch Footballer of the Year in 2014 and Ajax, who are delighted to be welcoming the player 'home', have not actually won a trophy since he left.
A United statement detailing Blind's achievements at Old Trafford finished with: "It goes without question that everyone at the club wishes him well for the future."