23-year-old Sakho is a France international, having played 14 times for his country since making his debut against England in 2010, while 20-year-old Ilori has played for Portugal at age-group level.
The pair have lifted the number of defenders signed by Brendan Rodgers during the transfer window to four, although Kolo Toure and Aly Cissokho missed Sunday's 1-0 win over Manchester United through injury.
Uruguayan centre-back Sebastian Coates has already been ruled out for most of the season with a knee injury. "I know the history of the club and the Premier League is the best league in the world, in my opinion,"
Ilori, who was born in London, said: "Liverpool have a great team and I think it's the place for me to be at the moment.
"I know 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."
No transfer fee was disclosed for either player, who join Toure, Cissokho, Iago Aspas, Luis Alberto and Simon Mignolet as new arrivals at Anfield since the end of last season.
However, reports suggested Liverpool paid £19.5m for Sakho and £7m for Ilori.
"My aim while I am here is to play in the Champions League with Liverpool," Sakho, who made 151 league appearances for PSG, scoring seven times, said.
"I remember their teams when they were in the competition when I was younger.
"The Champions League is a tournament that all the great clubs in Europe participate in and that's where we need to get to."
Eurosport France's Maxime Dupuis said: "He is not as technically gifted as some defenders but he is really, really tough. He's a beast and some forwards have admitted to being afraid of him in the past. Sometimes he makes mistakes but he's young. I think he could have a good future at Liverpool. The fee might seem a little bit high but he's a real player. Physically, he is very impressive."
Liverpool, who top the Premier League standings with three wins from as many matches to start the campaign, also picked up Chelsea winger Victor Moses on a season-long loan.
Moses said: "The most important thing is for me to be professional about it and I'm here to do a job for the club.
"The target is to get into the top four and for the club to compete in the Champions League - and I'm delighted to be here."