Michael, 48, was diagnosed with severe pneumonia in November and treated in the Austrian capital where he was taken ill.
He was forced to postpone his tour and spent several weeks in hospital, describing his illness as "touch and go".
On his Twitter feed, he wrote: "I've been a busy boy in the studio this week ... finally ready to write about what happened to me in Vienna ... and how grateful I am to be given another chance to live and breathe alongside you all in this wonderful world that we share."
He added that he wanted to repay the "unending kindness" his fans had shown him with new music, and said he had begun to write the track which will be called "White Light".
The "Careless Whisper" star announced last month that he was back in good health and would re-start his postponed "Symphonica" tour in September.
(Reporting by Mike Collett-White, editing by Paul Casciato)
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