The 32-year-old club captain and Town Foundation patron will succeed Jason Gillespie.
Australian Gillespie left at the end of the season after leading Yorkshire to the County Championship title in both 2014 and 2015.
This year they finished third, missing out on the title to Middlesex on the final day (Somerset were second).
Dewsbury-born left-handed batsman Gale has spent his entire career at Yorkshire.
He has been captain for the last seven years.
Former Australia fast bowler Gillespie, 41, had been coach for five seasons.
Under Gale’s captaincy, Yorkshire won promotion to Division One of the Championship in 2012 - Gillespie’s first summer in charge.
They were runners-up in 2013.
Yorkshire were beaten in the T20 Blast and One-Day Cup semi-finals this summer.
Martyn Moxon, the Yorkshire director of cricket, confirmed on Friday that a decision has been reached regarding the new coach.