The goalkeeper, who started the current campaign between the posts for the Magpies, has spent the last two seasons on loan at Swansea City, helping them to reach back-to-back Sky Bet Championship play-offs.
He kept 21 league clean sheets last term, earning him the Sky Bet Championship Golden Glove award, having recorded 12 shut-outs the season before.
Woodman, 24, signed a new three-year contract with the Magpies last summer. He joined United in 2013 and made his debut for the Reserves in a friendly as a 14-year-old.
He has made nine first team starts - four of them in the Premier League - in between gaining experience during loan spells with Crawley Town, Kilmarnock, Aberdeen and Swansea and amassing a combined 139 senior appearances.
Woodman has also played at every youth level for England, winning the 2014 UEFA European Under-17 Championship and the 2017 FIFA Under-20 World Cup and receiving the Golden Glove award for best goalkeeper at the latter tournament.
Former Newcastle midfielder Scott Parker is Bournemouth's head coach and they are currently third in the Sky Bet Championship.