Freedom of Information figures show the Scottish Funding Council (SFC) picked up the huge costs and expenses of Mr McLeish's office which was set up to run Glasgow's further education institutions.
Mr McLeish has been chairman of the Glasgow Regional Colleges Board since its inception two years ago.
The SFC covered the £104,000 bill for his staff, an office on Glasgow Caledonian University campus, and other costs.
Mr McLeish claimed a further £31,535 for national project work and expenses during 2012-13 and 2013-14. The total bill came to more than all of Scotland's other college regions put together.
Larry Flanagan, general secretary of the EIS teaching union, said: "Given the cuts that have occurred in further education, the last thing which lecturers wish to see is more money being spent on management functions rather than in teaching and learning."
Mary Scanlon, Scottish Conservative education spokeswoman, added: "This money is taken away from funding education and training. It is quite alarming, considering the drastic cutbacks in further education in recent years, that a regional board chair is spending thousands of pounds that are not seen as necessary by regional chairs in other areas."
Scottish Liberal Democrat spokesman Liam McArthur said that following budget cuts: "These figures will raise eyebrows, not least among staff and students across Scotland."
Mr McLeish's role was created as part of the Scottish Government's college merger programme which created 13 regions to give colleges a strong voice, provide a link with employers and universities and oversee merger plans.
They were due to save £18 million this year and a further £33m next year though more than £50m is being pumped into the sector to secure ongoing cost reductions.
Glasgow is one of only three multi-college regions along with Lanarkshire and Highlands and Islands.
Mr McLeish's board oversees three colleges institutions merged from seven original institutions.
Officials said Glasgow's unique demands required additional support. Mr McLeish was one of 13 regional leads appointed in July 2012.
A spokeswoman for the Glasgow Regional Colleges Board said the SFC directly funded two staff seconded to the body. A decision to set up an office in Glasgow Caledonian University to help ensure some neutrality had also added to costs. The university was paid directly by the SFC.
A government spokeswoman said: "The demands of regionalisation in multi-college regions are such that those regions require additional support and resource. Recognising the scale and complexity of the demands of strategic planning, the regional staff resources in Glasgow have been paid directly by the Scottish Funding Council."