Transport Minister Joram Gumbo justified the decision on the grounds that Mr Mugabe was a “war hero” and “African icon”.
There is tension about who will succeed the man in power since 1980, with a number of key contenders removed from their posts.
Mr Mugabe, 93, says he will stand for re-election next year.
His wife Grace has been tipped to succeed him and is expected to be appointed vice-president.
When plans to rename the airport were announced in September, Zimbabwean journalist Elias Mambo suggested the president’s ego was being “massaged”.
President Mugabe and his wife unveiled the new plaque bearing his name in a short simple ceremony.
The name change is just one of a series of events planned by the government to pay tribute the man who led the country to independence.
In August, the government announced plans to build a $1bn university named after him.
But the BBC‘s Shingai Nyoka in Harare says Zimbabweans are divided over the name change at the airport, and the opposition has described it as an insult.
President Mugabe thanked the government on behalf of his family, which he said “is not just my wife and the children it is the whole country”.