Siem de Jong ended his three-year Newcastle United career and rejoined Ajax.
The forward travelled to Amsterdam last week for talks with the club.
And United today confirmed that the proposed £4million deal had been completed.
De Jong has signed a three-year deal at the Eredivisie club.
A club statement read: "Siem de Jong has completed a permanent transfer to Dutch side Ajax.
"The 28-year-old returns to the Amsterdam Arena, where he made over 200 appearances before signing for the Magpies in the summer of 2014.
"In total, De Jong – who spent the 2016/17 campaign on loan at PSV Eindhoven – made 26 appearances for Newcastle, scoring twice."
De Jong had reported back for pre-season training hoping to impress United manager Rafa Benitez.
Speaking last month, the Holland international said: “I will talk to the manager because I want to prove myself at Newcastle.
"I still feel I haven’t started here. It bothers me that I haven’t been able to do that. I wish it was different, but I can’t change that now.
“I’m disappointed about my years here until now. I want it to be a different story.”