Ter Stegen, 34, has been rumoured to join Ajax since June, when it became known that Ajax's technical director, Jordi Cruyff, set his sights on a senior goalkeeper, with Ter Stegen and former Inter stopper Yann Sommer on the shortlist.
The deal hit a late obstacle when Barcelona and Ter Stegen couldn't agree on financial terms, specifically on taxes. The question was resolved after weeks, giving Ter Stegen the green light to leave the Barcelona camp in Birmingham for Amsterdam.
Ter Stegen joined FC Barcelona from Borussia Monchengladbach in 2014 and has made 423 appearances for the Catalan giants. The 34-year-old has won 20 trophies with Barcelona, including 7 Spanish titles and a UEFA Champions League trophy in 2015.
The German stopper joins Ajax on the back of their joint-worst points finish in the Eredivisie, with the Amsterdam outfit finishing in fifth with 63 points. The Dutch record champions qualified for the UEFA Conference League qualifying phase through the Dutch play-offs and advanced to the third round after beating Serbian side Vojvodina Novi Sad 8-2 on aggregate.
Ajax will face Irish outfit Shelbourne in the third round.
Ter Stegen is the fifth player to join Ajax this summer, following Daley Blind, Caio Henrique, Marcos Leonardo, Tolu Arokodare, and compatriot Julian Brandt, who joined on a free transfer last Friday.
The 34-year-old goalkeeper is still under contract with FC Barcelona until 2028.