Colleagues today praised his role in helping the city weather the recession and bringing the Green Investment Bank to Edinburgh and wished him well.
Cllr Buchanan, who had an operation earlier this year, said family and friends had persuaded him to relinquish his position as economic development convener – a job he has done since 2007 – in order to put his health first.
The full council meeting on Thursday will be asked to appoint fellow SNP councillor Frank Ross in his place.
Cllr Buchanan will continue representing Liberton/Gilmerton ward.
In a letter to SNP group leader and council deputy leader Steve Cardownie, he said: “It is with regret that I am writing to tender my resignation from the position of convener of economic development. It is a post I have held with immense pride for the last five-and-a-half years, but my family and friends have prevailed upon me to step down and take more time to concentrate on my health.
“With a heavy heart, I have agreed that is the best thing to do at this time. I will continue to proudly serve the constituents of Liberton and Gilmerton as their councillor.”
Cllr Buchanan quickly established himself as one of the leading figures in the coalition formed between the Liberal Democrats and the SNP to run the city in 2007.
He had been tipped to take over as SNP group leader if the SNP emerged as the biggest party in the elections earlier this year and current group leader Steve Cardownie became Lord Provost.
But in March he was diagnosed as having a brain tumour and underwent surgery at the Western General Hospital.
He stood for re-election despite his illness and was returned comfortably. He was also reappointed to the economic development post.
Cllr Cardownie said: “Tom has been responsible for taking the convenership on to a new level. He was instrumental in securing several major projects for Edinburgh, not least the Green Investment Bank.
“He also did a great deal to protect Edinburgh from the worst effects of the recession. He will be a hard act to follow.”
Labour council leader Andrew Burns said: “Tom should be hugely proud of the work he has undertaken as convener of economic development. The political leadership provided by Tom has resulted in initiatives to support our young people get into jobs or training, as well as generally supporting the city’s economic future.”
Tory group leader Cameron Rose said: “We wish him well. He can take satisfaction from having conducted the city’s economic development department through a difficult period.”