The 28-year-old centre-back captained Tamworth to the Southern Premier Division Central title last season.
Collard had signed for the Lambs in May 2022 from then-Southern Premier Central rivals AFC Rushden & Diamonds, where he had also been skipper.
He moved to Diamonds at the end of November 2018 having left Kempston Rovers.
He had previously played for a number of clubs in the Aylesbury area, including over 50 appearances for Aylesbury United, as well as at Chichester City whilst he was a student in that area.
He joined Kempston in December 2017 and made around 100 appearances for Diamonds and scored 12 goals.
Bedford director Jon Taylor and manager Lee Bircham told the club’s website: "The club has now managed to agree terms with a very experienced defender. He has been hot on our list of priorities since last season's campaign finished. We all know he has a wealth of experience at our level and above, with last season captaining the Tamworth side who impressively won step three. Alex is a born leader and with his technical abilities and leadership, as well as his reputation as one of the most talented players at this level and above, is a massive signing for the Eagles.
"We are thrilled to have Alex on board and look forward to seeing him in action on the field of play in pre-season. Alex is a marquee signing for the club and proves to each team that we aren't looking to tread water next season. With his impressionable character, we are really confident that he will be a valuable asset to our team and help us achieve our goals".
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