League One side Bristol Rovers have moved to sign the 21-year-old, who was on loan at the club last term.
Matthews impressed last season after reaching double figures for goals from the heart of the Spitfires midfielder.
His new manager Darrell Clarke has challenged him to continue his progress at the Memorial Stadium.
“Sam is a very talented young player whose progress I have monitored for a while now,” Clarke told the club website.
“He has worked hard and learnt a great deal from his time at Bournemouth and during his loan spell at Eastleigh in the National League last season.
“We had to compete with a number of other clubs for his signature and I am delighted that he has chosen to join us.
“His arrival will intensify competition for first-team places at the club and I look forward to working with him.”