Knighted in 1982 and raised to the peerage in 1994, he was Conservative MP for Scarborough and Whitby from 1966 until 1974, when the constituency was abolished.
He was then MP for Scarborough from 1974 until 1992, when he was succeeded by John Sykes.
The Scarborough and Whitby constituency was recreated for the 1997 general election, at which Labour's Lawrie Quinn beat Mr Sykes.
Current MP for Scarborough and Whitby Robert Goodwill said Lord Shaw was a hard-working MP.
"Many people in Scarborough will remember him with great affection," he said.
"I am very sad to hear of his passing. I met up with him in the first week after being elected in 2005 and he was pleased that we had taken the seat back for the Conservatives after eight years of Labour."
Michael Shaw was educated in Leeds and Cumbria before joining the family firm of chartered accountants WH Shaw and Sons in Dewsbury, West Yorkshire, and he worked there as a partner from 1945-1978.
He fought the Dewsbury constituency in 1955 as a Conservative but was unsuccessful. He then stood for Brighouse and Spenborough as a United Liberal and Conservative (the 'National Liberals') candidate in 1959 but lost to Labour’s John Edwards by just 47 votes.
Mr Edwards suffered a heart attack a few months later so a by-election was called in March 1960 and Lord Shaw won with a majority of 666 votes.
In 1964 he lost his seat but two years later, back as a Conservative, he successfully fought the Scarborough and Whitby seat.
Because of the time he had to spend in London, Lord Shaw left the family firm in 1978 to concentrate on his role as an MP. He was also a European Member of Parliament from 1974-1979.
In 1992 he gave up his seat and returned home for two years to spend time with his family.
In 1994 he was asked by the then prime minister John Major to go up to the House of Lords. He was created a baron for life, taking the title Baron Shaw of Northstead, of Liversedge in the County of West Yorkshire.
Married to Jean for 69 years, they had three sons, and he was a devoted grandfather.
He died peacefully on January 8 2021 at the age of 100, latterly living in Winchester.