
The League One side were one of a number of clubs linked with the former Celtic striker following his release from Parkhead.
The Premiership leaders invoked a clause in his contract which allowed them to terminate the one-year contract extension signed in the summer early.
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Hide AdWith them doing so before the close of the January transfer market it means Griffiths can sign for a team outside the window.
According to Sky Sports, he will sign a deal with Falkirk until the end of the season
The Bairns are struggling in League One and manager Martin Rennie will see the 31-year-old as the man to fire the clubs into the play-offs and back into the Championship.
Griffiths spent the first half of the season on loan at Dundee but underwhelmed.
He has scored 121 goals in 248 Scottish top-flight appearances.