Burrow (27) scored twice in eight league appearances for the Pilgrims during a loan spell from Chesterfield in 2011 and returns to the club nine years later with extensive National League and National League North experience to his name.
He was the Minstermen's leading goalscorer in 2019-2020 but, like the Pilgrims, suffered play-off heartache at the hands of Altrincham.
Reflecting on Burrow's arrival, United boss Craig Elliott said: "I am incredibly excited that Jordan will be joining Boston United.
"He is a fantastic leader and in my opinion, a proper old fashioned number 9 that we have been lacking over past seasons.
"He has a huge amount of experience and I am thrilled at how keen he was to secure this deal."
Burrow was present at the Jakemans Community Stadium on Wednesday afternoon to sign his contract and model the Pilgrims' brand-new Adidas home kit. Produced in association with Kitlocker, full details regarding United's new kit deal will be announced over the coming days.