The defender has called time on his days in Turin and looks set to join the London club ahead of the closing of the transfer window on Wednesday
On Sunday Grygera said he was hoping to secure a switch to Craven Cottage while confirming he was leaving Juventus.
A statement confirming the split has been released by the Italian side on Tuesday.
The note reads: "After four years, the experience of Zdenek Grygera at Juventus has terminated.
"The Czech player has rescinded his contract by mutual consent."
The 31-year-old joins a Fulham side which has endured a difficult start to the season under Martin Jol, having picked up one point from their opening three Premier League games.
The London club secured Europa League football, however, with a 3-1 aggregate victory over Dnipro.