The 23-year-old has signed a long-term contract with Liverpool after having passed a medical.
Sakho told Liverpool's official website: "I'm delighted to be here. I'd like to thank everyone for the welcome.
"I came here because the project that is in place at Liverpool interests me. I'm really looking forward to playing my first game."
"I'm really looking forward to cracking on with work and I can't wait to get on pitch," continued Sakho.
"I know the Liverpool fans are fantastic and while I was in France, it was clear for me to see they are amongst the best in England."
Sakho becomes Liverpool boss Brendan Rodgers' seventh signing of the summer transfer window, joining Luis Alberto, Iago Aspas, Aly Cissokho, Tiago Ilori, Simon Mignolet and Kolo Toure at Anfield.