The Rangers legend died at the age of 73 after battling illness.
Tributes have been pouring in from around Scotland, from former players, including a touching moment from Ally McCoist, and other personalities and stars across world football.
“Celtic Football Club has expressed its deepest sympathies following the sad news that former Rangers and Scotland manager Walter Smith has passed away after battling illness so bravely,” the club said on the official website.
“Clearly, this is absolutely devastating news and our thoughts and prayers are very much with Walter’s wife, children and wider family at this very sad time.
“Walter was a tremendous servant to Scottish football for so many years, and during his time as manager of the Scotland national side, he forged a close friendship with Celtic legend, Tommy Burns, who was part of the coaching set-up.
“Everyone at Celtic sends their heartfelt condolences.”