Hogg, 36, will be joined by Neil Coverley as assistant manager, with the decision announced to supporters at a meeting on Thursday evening.
The board announced the decision to supporters at a meeting on Thursday evening with acting chairman Bill Murray saying after discussing the situation the directors felt the new management duo could do a good job.
Hogg, a UEFA A candidate with the FAW, said: "I feel privileged to have been appointed manager of Colwyn Bay FC.
"This is a big club in North Wales and I know how fortunate I am for this to be my first job in management.
"The irony hasn't escaped me that my first job as a manager is with the club I first joined as a 20-year-old after being released by Everton.
"I've learnt a great deal during the last seven years as an assistant and I've given that role everything. I fully intend to do the same now whilst continuing my evolution as a coach and now manager.
"Neil Coverley has agreed to take the role of assistant manager and I'm delighted by that.
"He and I are really looking forward to working with all at the club and we aim to give our loyal fans something to be proud of on this journey."
Their first game in charge is at Clitheroe who also lost their manager this week when Stuart Mellish resigned, with Lee Ashforth taking caretaker charge, assisted by former Colwyn Bay player Dave Mannix.