Speaking to official Tamworth website www.thelambs.co.uk Alsop said, "It all came down to my personal and footballing lives fitting together".
Alsop - who had featured for the Shots in the last few pre-season matches - was also being chased by Tamworth manager Mark Cooper.
Alsop dropped out of league football last season after he was sacked from Oxford United following an incident involving a youth team player and a banana and many Shots supporters had been unimpressed with his performances in a Shots shirt and were lost for words when news broke that he'd been offered a contract.
It's believed that the Tamworth offer was on a part-time contract, which will allow him to continue studying a college course that he recently started.
Alsop may yet play at the Recreation Ground on the first day of the season as the Shots take on his new club in their opening fixture.