Streete was released at Newcastle by mutual consent.
He played three times for Vale last season and has now linked up with the League One side.
“We're really pleased to have signed up Remie. He's a very good player with a lot of potential – something we saw when he was last with us," Vale manager Rob Page said.
“We were very impressed when he was last with us and we made him one of our top summer targets so to have him in the building is brilliant."