The two clubs last month agreed an undisclosed fee for the player, who joined Liverpool from West Ham in 2007, and the deal has been confirmed this afternoon.
The 30-year-old Israeli international made 172 appearances and scored 37 goals during his three seasons with the Reds.
A Liverpool spokesman said: "Yossi's departure was agreed between the player and Rafael Benitez a number of weeks ago. Everybody at Liverpool FC wishes him well for the future."
It's done. He's now a Chelesa man. I'm too depressed to find pictures or anything. Brazil just lost.