Liverpool had announced the deal on Thursday, but it was subject to a medical and the signing of personal terms, both of which passed on Friday.
"I'm very happy to play for this big club," Assaidi said. "The first time I spoke to the coach I had a good feeling.
"I had offers from other big clubs but I've been waiting for this moment. The coach gave me a good feeling. It will be a dream to play with these big players and I hope training will help me to be a good player here.
"When I watch Liverpool it's always a good atmosphere, the fans are fantastic and I'm happy to be here."
Assaidi, 24, scored 10 Eredivisie goals from midfield last season and comes as a direct replacement for Maxi Rodriguez, who returned to Argentina.
Born in Morocco but raised in Holland, the former De Graafschap wide-man has played 22 times for his country, scoring once.
Rodgers had already signed Wales midfielder Allen from his former club Swansea and Italy forward Borini from Roma.
The Northern Irishman expressed his delight at the latest capture, although urged fans to be patient as Assaidi adapts to the Premier League.
"We're delighted with the signing, he's a young player who has done very well, in particular in the last couple of seasons, in Holland.
"He fits our style perfectly, he's an exciting player who is very good in one versus one situations and I think he's a player that will excite the crowd.
"We're not expecting too much too early, he needs time to adapt but we're delighted he's chosen to come here over a number of other clubs."