Grygera became the seventh of 10 new arrivals this summer, joining John Arne Riise and Pajtim Kasami in making the move from Serie A.
"You can see that football in England is different to football in Italy," said the 31-year-old, who will be hoping to make his debut on Thursday.
"It is a lot more physical over here and, in my opinion, the game is played at a higher level, although in Italy it is arguably more tactical.
"It was a great honour to play for a club like Juventus - one of the most renowned and successful clubs not just in Italy, but perhaps even the world.
"But, after four seasons in Turin, I am now concentrating on being here and doing well for Fulham."