The former Sale junior, who will replace Mike Peel when he retires at the end of the year, said: "It's fantastic golf club which retains its traditional values and I know I will fit in well there.
"I have plenty of ideas including setting up an indoor swing area and I can't see myself moving anywhere else."
Norcott, 36, who was professional at Cheadle where he was also an assistant as he was later at Northenden before moving to Davenport, has been involved in a business servicing the golf industry for the last 10 months.
"I'll relinquish that position but the experience will come in useful at Stockport where I'm going back to what I do best - teaching and looking after members," he said.
"I don't play as often as I used to but I'm looking forward to getting on the course because I had a hole in one there during an Open Championship region qualifier a few years ago."
Peel, who moved to Stockport 15 years ago after two decades at Bury, is an archetypical club professional although he enjoyed success as a player in his early career, winning the Manchester Championship and Northern Assistants' Tournament.
He was an assistant under Alan Gillies at Swinton Park, then Malcolm Hill at Hazel Grove, before being appointed pro at Buxton High Peak.
His two sons are also in the game - Jason is pro at North Manchester and David has made more than 100 appearances for Cheshire.
"I'm hoping to carry on teaching and will intend to play more," said Peel, who turns 65 next May.
Meanwhile, Simon Edwards is leaving Wrexham club Clays next month and heading for Windermere to replace Southport-born Steve Rooke who is retiring after 31 years.
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