Former Hibernian and Motherwell keeper Woods, 39, makes the step up after two years working with the club's reserve and youth sides.
The first team have been without a goalkeeping coach since Jim Blyth left Parkhead along with manager Gordon Strachan a month ago.
Tony Mowbray did not bring a specialist with him from West Brom and has instead decided to give Woods his big break.
Poland star star Boruc suffered a dramatic slump in form last season, making a series of high-profile blunders as Celtic failed to win a fourth straight SPL title.
Woods will now be tasked with getting Boruc, 29, back to his best and he revealed he has a number of tricks up his sleeve to do just that.
Woods briefly worked with the keeper last season while Blyth was away scouting and took the time to contact some of Boruc's old Polish coaches and build a series of 'Polish-themed' sessions which impressed Celtic's number one.
"When I was a player, I hated doing the same thing every day," Woods told the club's website.
"I could imagine how stale it would get as a coach if you were doing the same thing every day.
"The challenge is to always keep things fresh and interesting and to embrace the latest techniques.
"I keep an open mind with everyone and listen to any comments that people have about my coaching and with that approach I personally find work to be much more refreshing and rewarding.
"I do work on the fundamentals and will make sure they don't take the eye off the ball in that respect, but they will get a good, varied training regime."
Woods added: "When you are working with youth-team goalkeepers, as I have for the past couple of years, you tend to look more at the fundamentals.
"Now, at first-team level, I will continue to do that but will try and keep them motivated and ensure the variety is there, from the start to the end of the season.
"That's crucial, considering the workload they take on over the course of the year and I have a bank of drills that I want to do, with Artur, Lukas Zaluska, Mark Brown, Scott Fox, Daniele Giordano and Dominic Cervi all in mind.
"I will work with them individually on each of their strengths and weaknesses and will give them my full attention over the season."
Woods described his promotion as "a dream come true", adding: "I am absolutely delighted and I have realised an ambition of mine very, very early in my coaching career.
"I feel this opportunity is something I am ready for and I am really looking forward to the challenge of working with the new management team."
Woods would appear to complete Mowbray's backroom staff after he brought assistants Peter Grant and Mark Venus with him from West Brom.
Mowbray said: "I know that many people within the club have been highly impressed with Stevie's work in recent seasons and we are delighted to give him this opportunity to work with the first team.
"I have spoken to Stevie at some length about his new role. I too believe he has a lot to offer and I am sure he will make a great contribution to the first team."
Woods will begin his new job after completing a sponsored climb of Mount Kilimanjaro, which has seen him raise more than £4,000 for the Anthony Nolan Trust and their ongoing work and on
leukaemia and bone marrow transplantation.
"That was a stroll in the park," he joked.
"I think my biggest hill is now in front of me, working with some great goalkeepers in front of those incredible supporters. I can't wait to get started."