He took over at the Pilgrims in December last year, a month after leaving the Stags.
But following a 3-2 home defeat to Brackley Town and a run of one win from 11 National League North matches that saw Boston drop into the bottom two, Murray announced his decision to quit.
The Pilgrims had the fourth-worst defensive record in the division, despite a summer overhaul by the manager.
They did reach the fourth qualifying round of the FA Cup, including a narrow 1-0 win at AFC Mansfield.
And Murray also won praise for off-field changes at Boston, including improving the changing rooms and the club’s approaching to coaching and management.
Last season he helped to ensure the Pilgrims survived in the division, finishing 15th.
Murray left the Stags after two years as manager, ending an association with the club that stretched back more than 14 years.