Sissoko, 26, was born in France but represents Mali at international level and has never previously played in Ligue 1.
He enjoyed spells at Valencia and Liverpool before moving to Juventus in 2008 and has now penned a three-year deal at the Parc des Princes.
"For me, it's a huge pleasure to play at PSG," said Sissoko at a press conference where he was presented to the media alongside Sirigu.
"I chose this club because it's a club with a very ambitious project and the people here have told me some very important things."
Meanwhile, 24 year-old Sirigu, who has two caps for Italy, has signed a four-year contract after leaving Palermo.
"Why did I choose Paris? It's a club that wants to create something," said Sirigu, Italy's third-choice goalkeeper.
"I'm very happy to be here and to be a part of such a team. I'm honoured by the interest shown in me. The team is going in a direction that suits me."
Sirigu's arrival could be bad news for Nicolas Douchez, who arrived from Rennes last month as PSG's new first-choice goalkeeper but who will miss the start of the season through injury.
"It's important for a team like PSG to have goalkeepers capable of stepping up when the moment arrives," added Sirigu.
"I'm very happy to be able to play alongside Nicolas, who I've often watched on the TV, and I can't wait to train with him."
The moves are a further indication that PSG are determined to establish themselves as a major force following the arrival of Qatar Sports Investments (QSI) as majority shareholders and the appointment of Leonardo as sporting director.
The club have now made seven signings this summer, with Kevin Gameiro (Lorient), Milan Bisevac (Valenciennes), Blaise Matuidi (Saint-Etienne) and Jeremy Menez (Roma) already having put pen to paper.
More are likely to follow, with Leonardo reportedly close to agreeing a sensational 30 million-euro ($43 million) swoop for another Palermo player, Argentine playmaker Javier Pastore.