The 18-year-olds – part of the U19s side that faced Sri Lanka in three Youth ODIs earlier this month – have extended their deals until the end of October 2026.
Both impressed at the ICC Under-19s Cricket World Cup earlier this year in South Africa where leg spinner Ali was the fourth leading wicket taker.
He claimed 14 wickets in four games, including the best tournament figures of 7/29 against Zimbabwe, while all-rounder Wylie hit 61 in that final group game and also took 4/42 against Australia.
Warwickshire Performance Director Gavin Larsen, said: "We’re thrilled to be offering two of our graduating Academy players their first professional contracts.
“Theo is an excellent ball-striker and Taz a developing leg-spinner. Both show the attributes to feature in domestic cricket in the near future.
“Entering the Bears environment will accelerate their development and they’ll benefit from the full range of professional support to assist their growth. Where their ceiling ultimately is as cricketers will, like any sportsperson, be over to their individual drive and determination to be the best they can be.
Both Ali and Wylie are set to feature in Warwickshire’s Metro Bank One Day Cup campaign which gets under way at Essex on Wednesday (24 July) followed by trips to Leicestershire (26 July) and Sussex (28 July).
Bears then head to Rugby School on Friday 2 August where Surrey are the visitors. It’s the first time in almost a decade the Club has played a senior game at an out-ground away from Edgbaston.
Around 2,500 tickets have been issued for the game but tickets are still available.