The players had been out of contract in the summer, but will now stay on following the club's promotion from the Third Division.
The Cherries' manager Sean O'Driscoll is now hoping Maher can recapture the form he was showing for the side, prior to his injury last season.
"Shaun Maher's season was curtailed through injury," explained O'Driscoll. "We were just seeing the best of him when he was injured and he's been working extremely hard to get back.
"I see no qualms about him not being fully fit for the start of pre-season training on July 4 and it will be like signing an extra player if he carries on where he left off."
O'Driscoll believes O'Connor has vast amounts of potential and is hoping he can build on his excellent form for The Cherries.
"Garreth O'Conner has shown the ability that he knew he had this season," continued O'Driscoll. "He came back determined and has been exceptional.
"He's taken more responsibility on the pitch and he, together with the rest of the lads, can go on from strength to strength."
