Both players featured in Stoke's Under-21 side as they beat Getafe's B team on Sunday, with forward Telford scoring one of the goals in a 3-0 win.
He and Waddington, a central midfielder, were being set up for new deals at Bloomfield Road but have instead signed up with the Potters according to the Gazette, who say they inked deals at the Britannia before the Stoke first team headed off on their pre-season tour of Singapore.
Though neither club have confirmed the moves, the duo are believed to have trained alongside the first team a couple of weeks ago, and are now expected to join up with Stoke's development squad in the new season. Their switches may end up going to a tribunal if the two clubs can't agree a fee.
The Gazette state Mark Hughes already made a bid for Telford last season, while Waddington had been approached about a possible loan to Brighton in the coming campaign while still at Blackpool.
Both 18-years-old, the players featured in the Seasiders' disastrous relegation campaign last season, Waddington making 5 appearances and Telford managing to score once in 15 matches.