The 31-year-old has been with the Turin giants for the past four seasons and has now penned a deal with the Cottagers, with an option for a further year.
He moves on a free transfer after his contract with Juventus was terminated by mutual consent on Tuesday.
Grygera faced Fulham in March 2010 when he come off the bench during Fulham's 4-1 Europa League win against Juventus at Craven Cottage, which he is excited to now call home.
"I am delighted to have completed my transfer to Fulham Football Club," he told the club's official website, www.fulhamfc.com.
"It has always been an ambition for me to play in the Premier League and I am looking forward to an exciting new chapter in my career with Fulham."
Grygera began his career with Czech side FK Svit Zlin in 1997, before moving to Petra Drnovice and Sparta Prague.
The defender, who has made 52 appearances for his country, joined Ajax in 2003 and then Serie A outfit Juventus in 2007.
Source: PA