The 21-year-old is currently on loan at Whaddon Road, and has now completed a full-time switch.
"I am very pleased we have signed Scott. He is a player that I have been interested in for some time," said Robins boss John Ward.
"Scott can play in two or three different midfield positions and he wants to play regular first-team football.
"Hopefully that is something we can provide for him and I am sure that over the next two-and-a-half years he will become an important player for us."