Liverpool have signed central defenders Mamadou Sakho and Tiago Ilori for a combined fee of about £25m.
The Anfield club have also taken Chelsea forward Victor Moses on a season-long loan.
Sakho, 23, who has 14 France caps, will cost around £18m from Paris St-Germain.
London-born Ilori, 20, has represented Portugal at youth level but is still eligible to play for England.
Sakho told the club's 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."
He is manager Brendan Rodgers' most expensive signing of the summer and can play in the centre of defence as well as at left-back.
Liverpool managing director Ian Ayre said: "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."
Ilori, who cost £7m, said: "Liverpool have a great team and I think it's the place for me to be at the moment.
"There have been some great teams here in the past and the club has won a lot of trophies and I want to be a part of it."
In other transfer news Martin Demichelis admitted the chance to join Manchester City and be reunited with Manuel Pellegrini was too good to turn down.
The 32-year-old Argentinian defender has joined the 2011/12 Premier League champions on a two-year contract after City prised him away from Atletico Madrid, the club he joined earlier in the summer as a free agent.
City missed out on recruiting Demichelis without a fee being involved and will have compensated Atletico for the loss of a player they only briefly knew.
However, Pellegrini was keen to bring the player he has previously coached at River Plate and Malaga to the Etihad Stadium, and Demichelis hopes he can play a big part in the club's pursuit of silverware under the Chilean manager.
Stoke have confirmed the signing of 24-year-old Austria forward Marko Arnautovic on a four-year contract from Werder Bremen.
West Brom have secured the services of 28-year-old midfielder Morgan Amalfitano on a season-long loan from Marseille with an option to make the deal permanent.