Alan Pardew has been chasing the versatile 23-year-old for much of the summer and will now discuss personal terms with Anita, who can play at full-back or in midfield.
Anita told reporters following Ajax's 2-2 draw with AZ Alkmaar: "The clubs have a deal, I think £6.6m. Now I have to reach an agreement with Newcastle, I have an offer, but I cant say more about this.
"The clubs have agreed a fee, but I have not. I'm still an Ajax player. I think it will be finished soon, but you never know how it will go.
"Now it's up to me. But first I want to talk with the manager of Newcastle United before taking a decision. The whole picture has to be right for me."
Anita's signature would represent Newcastle's biggest transfer fee of the summer after failed attempts to sign Lille defender Mathieu Debuchy.