Sakho's arrival on deadline day follows the earlier arrival of Tiago Ilori, who has signed from Sporting Lisbon for a reported fee of £7million.
They take the total number of players brought in by Reds boss Brendan Rodgers this summer to seven, following Kolo Toure, Iago Aspas, Luis Alberto, Simon Mignolet and Aly Cissokho.
Sakho played 201 games for PSG, securing the Ligue 1 title with the capital club last season to add to winners' medals for the 2010 Coupe de France and the 2008 Coupe de la Ligue.
But now the 23-year-old, who can operate in central defence or at left-back and has won 14 caps for Les Bleus, cannot wait to get started for his new team.
"I'm delighted to be here," he told Liverpool's website. "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."
He continued: "I'm really looking forward to cracking on with work and I can't wait to get on (the) pitch.
"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."