The 31-year old Czech Republic defender was a part of the Juventus team which the Cottagers overran to win 4-1 in the Europa League in March 2010 – the victory giving the Londoners a 5-4 aggregate win against the odds in the Round of 16.
And now he has arrived at Craven Cottage, Grygera hopes he can be part of a successful side as Fulham get ready for another Europa League campaign which kicks off at home against FC Twente on Thursday.
"Fulham turned a lot of heads when they knocked Juventus out of the competition and I've taken an interest ever since - when you are involved in a game like that it is only natural," Grygera told the club's official website.
"It was a difficult night for those on the losing side but, of course, it was a special night for Fulham.
"I've played a few times against English teams over the years and, every time, I have been struck by the atmosphere in and around the grounds, and Craven Cottage was no different.
"Even though it is small in comparison to some, the atmosphere was fantastic and made for a great setting.
"It's funny how things work out. It shows that in football you just never know what will happen.
"I'm very happy to be opening a new chapter in my career and hopefully I can share similar lasting memories with the fans."