In April, Neil Baxter, secretary of the Royal Incorporation Of Architects In Scotland, reported Mr Matheson to the country's ethics watchdog over his handling of the design competition, which was for a £15million revamp of the civic area.
The leader was accused of misconduct, interfering in a legally binding procurement process, attempted staff coercion and trying to steer the contest in favour of his preferred design.
However, Standards Commissioner Stuart Allan has now cleared him on all counts.
His report states: "Councillor Matheson did not engage inappropriately in the management of the competition to select the design for the redevelopment of George Square and did not act unfairly in applying his own judgement to the selection process.
"The council - and the council alone - were responsible for approving a design and deciding whether to proceed with construction. The council was not bound to go ahead with the designs submitted to the competition.
"The project, after all, attracted diverse views from the citizens of Glasgow and the total cost at an estimated £15m was a major consideration.
"The decisions to conclude the competition process and to proceed with a less ambitious scheme were properly taken and Councillor Matheson's conduct in relation to these decisions was appropriate."
Mr Matheson said he was delighted but not surprised to have been cleared.
He added: "I was right to listen to the views of the people of Glasgow and the commissioner has said I had a responsibility to do that.
"The people of the city were clear they wanted the Square to be better, but not radically redesigned, and that is what we have delivered."
Mr Baxter said he was appalled at the decision and added: "It casts doubt on whether the commission is working in the public interest or simply to bury bad news."