Ajax confirmed the arrival of the 34-year-old on loan from the Spanish champions, with the move finally completed after Barcelona and the player resolved tax-related issues that had delayed the transfer.
In a statement, Ajax said: "Ajax has reached an agreement with FC Barcelona and Marc ter Stegen. The 34-year-old goalkeeper joins the club on a season-long loan from the Spanish side."
Ajax technical director Jordi Cruyff welcomed the signing and believes the former Barcelona captain will make an immediate impact.
"Marc has an outstanding track record, and his qualities are widely recognised. He is an immediate addition to our squad," Cruyff said.
"Marc and I know each other well, and I'm looking forward to working with him again.
"We have been working on bringing him here for quite some time, so we're very pleased that he has signed his contract and can now get started."
Ter Stegen travelled to Amsterdam after leaving Barcelona's pre-season training camp in Birmingham and completed his medical before the deal was officially announced.
The Germany international joined Barcelona from Borussia Monchengladbach in 2014 and established himself as one of the club's greatest goalkeepers. He made 423 appearances, won 20 major trophies, including seven La Liga titles and the UEFA Champions League in 2015, and captained the side.
His opportunities became limited after Barcelona signed goalkeeper Joan Garcia, prompting the search for regular first-team football.
Ajax hope Ter Stegen's experience will help them recover from a disappointing Eredivisie campaign in which the Amsterdam clubs finished fifth with 63 points, equalling their joint-lowest points total in the competition.
The Dutch giants have already progressed to the third qualifying round of the UEFA Conference League after defeating Vojvodina Novi Sad 8-2 on aggregate and will now face Irish clubs Shelbourne.
Ter Stegen is Ajax's latest signing of the transfer window, joining Daley Blind, Caio Henrique, Marcos Leonardo, Tolu Arokodare and fellow German Julian Brandt.
The goalkeeper remains under contract with Barcelona until 2028, with the Spanish clubs continuing to pay the majority of his wages during the loan spell.
