Skriniar joins in a Bosman deal, having initially committed to PSG in January.
He said at his presentation: “The last few months were not easy for me, I was injured, I had a back problem but now I feel really good. I played two matches with Slovakia, so I am ready. I haven't stopped training since the injury, so I am 100%, maybe even more.
“When a club like Paris Saint-Germain wants to sign you, you have to make a decision quickly. I know they're one of the best teams in the world, it only took a second."
Skriniar added: “There is always pressure when you arrive at a club like Paris Saint-Germain. I feel it a little bit, but I feel ready, ready to be part of this great club. I like the pressure, I always try to be ready."