The former Newcastle United defender replaced Neil Aspin at the International Stadium ending his relationship with Macclesfield Town.
The Vanarama National League leaders will be an attractive proposition and Askey is proud of the part the Silkmen have played in getting the 43-year-old on the managerial ladder.
Watson's exit creates a vacancy and the Macc manager told the club's website that he hopes to fill the role before long.
He said: "It's a shame to be losing Steve but we all wish him well. It's a great opportunity for him, I feel Gateshead are underachieving with the players they've got. He wanted to go into management and it's as good a job as he could've got.
"It's pleasing in some ways that we've done well and given somebody a chance to progress their career, so from the football club's point of view it's a good thing although we would've like Steve to have stayed.
"With anybody who comes in we're quite open and we allow people to show what they can do and it was the same with Steve. He came in and had to get used to us and our ways. He's done that and hopefully he's taken something with him whilst being with us.
"If he can do well at Gateshead then I'm sure he can get a more lucrative job in the future."