The Reds have secured the Frenchman on a season-long loan from Valencia and, despite having played for some of Europe's top clubs already in his career, the left-back describes the move as a "dream".
"I feel extremely proud to be here and I'm proud of all the hard work I've put in so far throughout my career," Cissokho told the club's official website.
"I've always dreamt of one day signing for a really legendary club. I've been lucky enough to play for a few top sides and so to now get the chance to play for a club like Liverpool, it's just fantastic.
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"It's really pleasing when a club like Liverpool shows interest in you and, when that interest becomes more serious, you really can't wait for the move to go through. Now that the transfer has been completed, I'm really happy.
"I hope to feature in as many games as possible. I know it's going to be quite tough and I need to get to work as soon as possible as pre-season is over and we are into the league programme."
Cissokho played for Olympique Lyonnais when they beat Liverpool 2-1 back in 2009 and says that he has good memories of Anfield as a result.
"I was fortunate enough to play at Anfield and it was a really special occasion for me," the defender enthused. "I have some great memories of that night. Although it was us that grabbed the win, it still remains a good memory.