The 74-year-old revealed he is suffering from bladder cancer and will have an operation in early October.
Sir George, who is currently the Lord Lieutenant of Clackmannanshire, said he remained "in good spirits" and was "optimistic", thanking "all who have sent their best wishes".
In a statement, he said that he would need "several months of convalescence" and, while asked to continue as Lord Lieutenant of Clackmannanshire, his duties would be carried out by the Vice Lord Lieutenant, Lady Mar, and his deputies until further notice.
Sir George, who was knighted last year for "services to Scottish politics and public life", has also stepped down from his positions as Electoral Commissioner, chair of the Remuneration Board of the National Assembly for Wales, trustee of Glasgow Life and chair of Alloa Community Enterprises (ACE).
He has had to cancel all public engagements for the time being. Malcolm McArdle, ACE Managing Director, said yesterday: "The board, management and staff at ACE would like to thank George for his contribution and wish him good health for the future.
"We are deeply sorry to be losing Sir George as our chair. His commitment to social enterprise and to Clackmannanshire has been exemplary, however, his health must come first and all at ACE send their best wishes for his speedy recovery".
Clackmannanshire Provost Tina Murphy said: "We respect the family's desire for privacy, and send George every good wish for successful treatment and a speedy recovery."
Sir George served as the second Presiding Officer of the Scottish Parliament between 2003 and 2007.