كتب : وكالات
The 30-year-old Denmark international moved for a fee of €4.5million to become Roy Hodgson's fifth summer capture.
He joins Milan Jovanovic, Joe Cole, Jonjo Shelvey, Danny Wilson and Fabio Aurelio, who re-signed after being released.
The arrival of Poulsen could see defensive midfielder Javier Mascherano go after he expressed his desire to leave Anfield.