The 26-year-old is one of a number of new faces at Anfield after the summer signings of Charlie Adam, Jordan Henderson and Alexander Doni.
Houllier, who has managed both clubs, told BBC Sport: "Stewart will fit in very well at Liverpool. I like him very much as a player and I'm certain he will be a very big asset to them.
"Stewart is very, very professional. He takes on board everything you tell him and is very intelligent about the game."
Liverpool have now spent over £100m since the arrival of American owner John W. Henry last October.