The 53-year-old will leave his current post with Motherwell and take up his new role next month.
Wolecki Black is targeting promotion from SWPL2 before he leaves, with his Motherwell side holding a 13-point lead over nearest rivals Kilmarnock.
Celtic Women lie third in the Scottish Women’s Premier League, with Glasgow City and Hibs Ladies occupying the top two spots.
Speaking to Motherwell’s website, Wolecki Black said: “I had a very difficult decision to make and I leave with a heavy heart. It’s a big opportunity – a huge honour to join a club of Celtic’s stature.
“I’m staying with the team with a view to staying with them until the title is won. They are in a very good position and I want to see it through.”
Wolecki Black made his mark during a 14-year spell with Glasgow City, with whom he won four league titles, four Scottish Cups and four League Cups.
He suffered a stroke in March 2016 while in charge of Airdrieonians, then in League One, but was appointed manager of Motherwell Ladies eight months ago as he continued his recovery.
David Haley has brought the curtain down on his five-year tenure in charge of the Celtic ladies team and will now focus on the club’s Girls’ Academy. Edward Gallagher will take temporary charge in the meantime.