Finn, who was the Queen's representative in the province from 1987 to 1994, died Wednesday at the age of 94.
Finn was considered a leading Acadian figure in the province who helped champion health and education and was an advocate for the development of the Dr. Georges-L.-Dumont Hospital Centre in Moncton.
He was a former rector at the University of Moncton and was named a member of the Order of Canada in 1974 and an officer in 1979.
In 2008, Finn said he would return his Order of Canada to protest Dr. Henry Morgentaler's receipt of the distinction because he believed bestowing the honour to the abortion rights advocate decreased the award's value.
Premier Brian Gallant offered his condolences after hearing of Finn's death.
"We offer our sympathies to the friends and family of Gilbert Finn," he said. "Mr. Finn did much for the province and the country."