Poulsen completed a £4.5m switch from Juventus yesterday, penning a three-year contract to become Hodgson’s fourth acquisition of the summer.
The Denmark international, 30, has played in the other three top European leagues and was first signed by Hodgson in 2000 when the Englishman was in charge of FC Copenhagen.
A tough-tackling player who operates in front of the back four, he is seen as a replacement for Mascherano, who is hankering after a move to Italy or Spain.
The Argentina star is being tipped to move to Barcelona in exchange for £15m and former Arsenal midfielder Alexander Hleb.
Poulsen endured a difficult spell in Italy but previously enjoyed successful spells in Germany and then Spain with Schalke and Sevilla.
His career began in his native Denmark, however, when Hodgson signed him up following a trial and the youngster’s aggression helped to secure the league title.
Poulsen has a chequered disciplinary record and was involved in an infamous incident that prompted a Danish fan to attack the referee during a Euro 2008 qualifier with Sweden. At 3-3 in the 89th minute Poulsen punched Markus Rosenberg, prompting the official to award a penalty and show the red card and, post-pitch invasion, abandon the match, awarding Sweden a 3-0 win.