The 25-year-old, who began his career at hometown club York City, has since played extensively for Harrogate Town and Alfreton Town during recent seasons.
He was part of the Harrogate squad which, like the Pilgrims, reached the play-offs in 2015-2016.
Platt has become the second Alfreton player to swap the Impact Arena for The Jakemans Stadium, following Luke Shiels' earlier move, and manager Craig Elliott was delighted with his latest signing.
"Tom is another experienced player who has played in this league for five seasons," Elliott told bufc.co.uk. "He can play a couple of roles in midfield and he knows what Boston United is all about from playing against us for other clubs.
"He is hungry to be successful."