The 33-year-old ended a six-year stay at Bundesliga side Schalke, where he scored 126 goals in 240 games.
Huntelaar netted 102 times between 2006 and 2009 in his first spell at Ajax, who lost in the Europa League final against Manchester United this season.
"It is no secret that Ajax are my club. I am very happy to be back here," said Huntelaar, who has 76 Netherlands caps.
The former Real Madrid and AC Milan front man added: "I won cups with Ajax but not the league title. The goal is to have that trophy at the end of the season, along with the rest of the team.
"I feel very fit and I'm already looking forward to the end of June when the preparation starts."
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Dutch striker Klaas-Jan Huntelaar has rejoined Eredivisie side Ajax after signing a one-year deal.