The versatile 24-year-old - who was Hereford's player of the year last season where he featured against the Pilgrim twice - has been in the manager's sights for a number of years.
"We have kept an eye on Ben for the last three years," Cox told bufc.co.uk.
"I have always been impressed with his performances in midfield, at centre-half and even at right-back. The versatility is important.
"Ben was voted supporters player of the year at Hereford – and is a great age."
Pollock came through the Newcastle United youth system and has been on the books of Hartlepool United, Dunston UTS and Billingham Synthonia before joining the Bulls.
"Ben is a fine footballer in his own right, who I believe will really flourish here at Boston United," Cox said.
Pollock is the son of former Premier League footballer Jamie, who featured for Middlesbrough, Bolton Wanderers, Crystal Palace and Manchester City.
Pollock follows striker Jordan Burrow into next season's squad.