Poulsen has helped Ajax win back-to-back league titles since his arrival in 2012, but the Denmark international has admitted that he is keen to end his spell in Amsterdam on a positive note.
The 34-year-old told the club's official website: "It was a difficult decision because I'm really enjoying myself at Ajax. My family is too. We think that it's a nice club with great people.
"We wanted to think carefully about it. My decision was taken with my brains instead of my heart - if I had gone the latter, then I would have re-signed.
"But I want a nice way to say goodbye and I do that now, as a fit player with another championship."
Poulsen, who spent a year with Liverpool during the 2010-11 campaign, has made 42 appearances this season.