Chelsea forward Moses has joined Liverpool on a season-long loan, while the two defenders are on permanent deals.
France international Sakho joins from Paris Saint-Germain and provides further defensive options for boss Brendan Rodgers - who also signed Tiago Ilori earlier on Monday.
The 23-year-old Sakho came through the youth system at PSG in 2007 and made 201 appearances during his career in the French capital.
He picked up a Ligue 1 winners medal last season but the lure of securing UEFA Champions League football with Liverpool has attracted him to the Premier League.
"I'm delighted to be here. I'd like to thank everyone for the welcome," he 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.
"My aim while I am here is to play in the Champions League with Liverpool.
"The Champions League is a tournament that all the great clubs in Europe participate in and that's where we need to get to.
"I hope to create a new piece of history with our supporters at Anfield."
Liverpool's managing director Ian Ayre welcomed the signings.
"Sakho is a top, top centre-half and that adds to the great centre-back pairings that we have already and it will give that depth," said Ayre.
"He's an important marquee signing for us. It was a difficult one to do and it was a difficult one for us to get, but I'm very pleased that we've been able to attract him to the football club."
On Ilori, Ayre said: "He's a young player, who has some experience, but he'll obviously need more.
"But he adds to that group of central defenders and he gives us something for the future as well as being someone who is able to contribute now."
