Goal understands the Reds will pay €17 million for the France international, who watched Sunday's 1-0 win over Manchester United at Anfield before completing his move
Sakho was at Anfield to watch the Reds' 1-0 win over Manchester United on Sunday, along with Tiago Ilori and Victor Moses, who is expected to complete a season-long loan move from Chelsea.
Goal understands Liverpool will pay €17 million for the France international, having seen off stiff competition from Roma for his signature.
"I'm delighted to be here. I'd like to thank everyone for the welcome," Sakho told the club's official website.
"I came here because the project that is in place at Liverpool interests me. I'm really looking forward to playing my first game."
Sakho becomes Brendan Rodgers' seventh signing of a busy summer, joining Simon Mignolet, Kolo Toure, Aly Cissokho, Luis Alberto, Iago Aspas and Ilori at Anfield.