The 22-year-old has penned an extension which will keep him at St. James’ Park until the summer of 2021.
And he will now link up with Championship side Swansea, who begin their campaign with a home game against Hull City at the Liberty Stadium on Saturday afternoon.
England Under-21 stopper Woodman has made four appearances for the Magpies to date, including three last term in the Emirates FA Cup.
He has also spent time out on loan at Hartlepool United, Crawley Town, Kilmarnock and Aberdeen in recent seasons, making a total of 35 outings during his temporary stints away from Tyneside.
Woodman, who featured for Steve Bruce’s side in their pre-season games against Wolves and Preston in recent weeks, was also part of the England Under-17 squad that won the European Championships in 2014, before lifting the Under-20 World Cup with the Young Lions – as well as the Golden Glove award – in 2018.
He could make his debut for Steve Cooper’s men when they entertain the Tigers in south Wales at the weekend.