
The 26-year-old Dodd signed on with the Bairns in March 2006 and made 25 appearances for John Hughes' side.
Phoenix coach Ricki Herbert said on the club's website: "Karl has played well in the top flight in Scotland and is technically very sound."
Dodd's last Bairns appearance saw him red carded in the 2-0 defeat by St Mirren in April. <!-- E SF -->
Meanwhile, Falkirk will allow striker Alan Gow to turn out for new club Rangers in Los Angeles - despite still being contracted to the Bairns.
Gow travelled with his new team-mates to the US for an end-of-season tour.
The SFA have confirmed that Gow - who signed off with a goal in Saturday's final SPL match against Dunfermline - can feature against LA Galaxy for his new club this week.
Sandy Bryson, the head of the SFA's registration department, confirmed that Gow can play in the glamour friendly.
Guest appearances in friendlies are allowed, if the player's parent club give the green light.
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ive got a song that wont take long, Adelaide are rubbish.. the second verse is same as the first.. ADELAIDE ARE RUBBISH
Oi Oi Edgecumbe... lets have a clean sheet
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