Poulsen seals Liverpool switch
The Premier League club's website said the 30-year-old had joined from Juventus where he spent two disappointing seasons after leaving Sevilla.
Juventus said Liverpool had agreed to pay a fee of 5.4 million euros for Poulsen. A further 1.2 million euros could be payable depending on appearances.
Poulsen, who has been capped 77 times by Denmark, plays a similar role to Javier Mascherano and his arrival will increase the likelihood the Argentine is to leave Anfield.
Hodgson, who has also signed midfielder Joe Cole from Chelsea and winger Milan Jovanovic from Standard Liege on free transfers since taking over last month, worked with Poulsen at FC Copenhagen.