
Stevens, 53, on Monday named family reasons, to be closer to his wife who is ill and reportedly requires another operation in the near future.
PSV director Jan Reker said that Stevens will sign a contract until 2010 at the club he played for 1975-1986. Stevens also coached PSV youth teams until 1993.
Eindhoven are without a coach since Ronald Koeman went to Valencia last month. Jan Wouters is acting as caretaker with Sef Vergoossen to take over in January for the rest of the season until Stevens' summer arrival.
"It was a difficult decision which we made with the family. Hamburg did everything to renew the contract but that was not possible," said Stevens, whose family home is just a few minutes away from Eindhoven's training ground.
Stevens came to Hamburg last February and led them from last place into the UEFA Cup. Hamburg currently lie third in the Bundesliga just one point behind frontrunners Bayern Munich. Stevens promised that he wants "to bid farewell in a decent way" in Hamburg.
Hamburg board chairman Bernd Hoffmann said: "There are more important things than winning points, and that is the family. I have great respect for his decision and would have acted in the same way."
Stevens won the UEFA Cup in 1978 as a PSV player and again in 1997 as a coach, with German club Schalke 04.
DPA