The 34-year-old goalkeeper has been linked with Ajax since June, when the club's technical director, Jordi Cruyff, identified the need to sign an experienced goalkeeper.
Ter Stegen and former Inter Milan keeper Yann Sommer were both considered, but Ajax have now moved forward with the Barcelona captain.
Several reliable reports claim the agreement was completed on Friday, with Ter Stegen expected to travel for a medical before the move is officially confirmed. The loan deal does not include an option for Ajax to make the transfer permanent.
Barcelona are expected to cover between 75 and 80 per cent of the goalkeeper's annual salary, which is reported to be around 15 million euros. The agreement also includes performance-related bonuses linked to appearances and Ajax securing qualification for the UEFA Champions League.
The move will see Ter Stegen reunite with head coach Michel, who took charge of Ajax in June after leaving Girona. The pair briefly worked together earlier this year when the German joined Girona on loan in January. However, his spell was cut short after he suffered a hamstring injury in February, limiting him to just two appearances before his season ended.
Ter Stegen has spent more than a decade at Barcelona after arriving from Borussia Monchengladbach in 2014. During his time at the Spanish club, he made 423 appearances and established himself as one of Europe's most consistent goalkeepers.
His impressive trophy haul includes seven La Liga titles and the 2015 UEFA Champions League crown, along with a total of 20 major honours.
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