His resignation follows Saturday`s 3-2 defeat to Brackley Town at the Jakemans Stadium.
Murray was appointed manager in December 2016.
The former Mansfield Town boss replaced Dennis Greene in the Pilgrims' hot-seat following a long spell at Field Mill which had begun as a player.
The season has not panned out how he would have wanted it to but last week went on the record saying he can turn things around.
Boston will release a statement soon outlining the way ahead, the club have confirmed.
His playing career started at Derby County and included spells at Notts County, Burton Albion, Kidderminster Harriers, Mansfield, Carlisle United, Torquay United, Oxford United and Luton Town.