Billy responded to a letter from Lord Provost Sadie Docherty that she had sent following the news he had surgery for prostrate cancer.
As reported in later editions of yesterday's Evening Times, Billy is also being treated for the "initial symptoms" of Parkinson's Disease.
The 70-year-old, who was given the Freedom Of The City Of Glasgow in 2010, said he was touched to receive the message.
He wrote: "I was very touched to receive a get well message from the Lady/Lord Provost.
"Please convey my best wishes to her."
The Lord Provost's message said: "I read today of your recent health difficulties and was pleased to learn you are on the mend following surgery.
"On behalf of the people of Glasgow, who welcomed you so warmly when you were made a Freeman of this city, I send our very best wishes and support to you and your family."
Celtic Football Club also sent its best wishes to their famous fan.
A statement on the club's website read: "Everyone at Celtic would like to pass on our thoughts and best wishes to Billy Connolly."
Former Celtic star Stiliyan Petrov wrote on social networking site Twitter: "Thoughts and prayers are with you Billy."
Despite his cancer operation and Parkinson's diagnosis, the star's spokeswoman said Billy would continue working and would shortly be starting filming for a new TV series as well as going on a tour of New Zealand in the New Year.
Singer Bob Geldof said his "great friend" would not be deterred by the diagnosis.
He said: "He's helped me lots in my endeavours. Pam and Bill are great mates. He's as strong as an ox mentally from everything he has been through as a kid. So I don't think this will deter him from being that individual we know."
Billy had what was described as "minor surgery in America" after being diagnosed with the very early stages of prostate cancer.
His spokeswoman said: "The operation was a total success, and Billy is fully recovered.
"In addition, Billy has been assessed as having the initial symptoms of Parkinson's Disease, for which he is receiving the appropriate treatment."
Steve Ford, chief executive at the charity Parkinson's UK, said: "One person every hour will be diagnosed with Parkinson's in the UK. Despite this it remains a little understood condition and we salute Billy's bravery in speaking out about his condition at this difficult time."