Poulsen moved to Amsterdam in August 2012, and has helped Ajax claim back-to-back domestic titles.
He has made 42 appearances in all competitions this season, providing an experienced head in an otherwise young midfield for Frank de Boer's men.
The 34-year-old's contract will expire at the end of the campaign and, although the club were keen for him to extend his stay, Poulsen is ready for a new challenge.
"It was a difficult decision because I'm really enjoying myself at Ajax," he told Ajax's official website. "My family also. We think it's a nice club with great people.
"We wanted to think carefully about, my decision was taken with my brains instead of my heart, if I had gone the latter than 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.
"I do not know what I'll do. My feeling sends us to Denmark, but that would mean that I would stop playing football altogether.
"I have not decided yet. If a club comes from another league, then we will certainly think about."
