The 24-year-old is out of contract and joins the League Two club on a free transfer.
Heed boss Steve Watson will now turn his attention to adding to his ranks after the loss of one of the club’s most consistent players.
“I’m looking forward to the challenge,” Montgomery said after signing for the 2017 National League Promotion Final winners.
“It’ll be the first time in League football for me and it looks like the club’s going in the right direction. I’m just really happy to be here and really looking forward to pushing on.
“Looking at the way the team plays and the style of play the manager has – I think that suits me, so hopefully I can come in and play the way the manager wants us to play.”
PICTURE: FOREST GREEN ROVERS FC