He won City's Player of the Year award in 2000 after establishing himself as one of the top centre backs in Division Three under Warren Joyce, but has since been more frequently used as a midfielder.
It was the promise of being able to play in his favoured defensive position on a regular basis that tempted him to join Boston.
The 27-year-old made over 200 appearances for City in all competitions during his time here, and scored 12 goals.
Meanwhile Mike Edwards and Paul Musselwhite could also be on the move. They have both been left sidelined since Jan Molby's appointment, and are rumoured to be on their way to Oxford and Boston respectively.
What do you think of this news? Do you think it's wrong to get rid of players of Greaves' and Edwards' calibre, or is Molby correct to do this? Discuss it on the message board.