The back-up stopper, who is the son of ex-Bairns sporting director Gary Holt, failed to make an appearance in his time at the club.
Last season, he played a handful of games out on loan at Scottish Lowland Football League side Dalbeattie Star.
A club spokesperson said: “We would like to thank Luke for his efforts while at Falkirk and wish him all the very best for the future.”
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Meanwhile, youth prospect Pearse Carroll has signed his first professional deal.
The 16-year-old midfielder has came off the bench in two of Falkirk’s pre-season matches and has impressed boss John McGlynn.
He has been handed a two-year deal and moves up from the club’s under-18s side.
McGlynn said: “We invited four of the under-18 players to take part in our pre-season training and we could immediately see the quality that Pearse has got. He’s a central-midfield player with an amazing left foot.
"He’s not the biggest and not the most athletic but he has great ability and we feel that, at 16, there are other attributes we can add. He’s definitely one for the future but depending on how well he develops, he may kick on quicker.”