The 17-year-old, who joined the League Two club towards the end of November, was an unused substitute in the Magpies' defeat at Darlington on Tuesday night and made a total of 11 appearances for Ian McParland's side.
Wedderburn impressed McParland when called upon, especially when Adam Nowland and Gavin Strachan were out injured, and the Scot has not ruled out a move for the promising youngster again next season.
"Nat has gone back to Stoke, so first and foremost I would like to thank him for his hard work with us and also Stoke City for allowing him to spend time at Meadow Lane," McParland told the club's official website. "Nat has done a good job when we have called on him and I do believe he has a good future at Stoke.
"He's certainly grown up while he has been with us and I am sure having experienced first-team football at such a young age will stand him in good stead.
"He told me he really enjoyed himself here which is really pleasing to hear, and we have also told Nat that we will keep monitoring his progress back at Stoke."