Mr Aspinwall had been diagnosed with cancer and passed away at his home in Willsbridge near Bristol, surrounded by his family earlier on Tuesday.
He represented the former Kingswood constituency from the May 1979 general election until his retirement in 1997.
Mr Aspinwall had previously stood as a Liberal Party candidate but changed his political allegiance in 1979.
He had represented Kingswood between 1979 and 1983 and, after a boundary change, the then Wansdyke constituency between 1983 and 1997.
The seat was lost to Labour's Dan Norris in 1997 before the constituency, which again became Kingswood, was regained by the Tories in 2010 by Chris Skidmore.
Paying tribute, the Conservative MP said Mr Aspinwall inspired him to enter politics.
"I first helped out leafleting for him when I was 11, and he chaired my selection as the Conservative candidate in Kingswood in 2008," he said.
"He was delighted that Kingswood had a Conservative MP once more, and was always there to help, to pass on his wisdom and experience that I was so grateful for.
"My thoughts go out to Brenda, and Jack's family, but I am sure that they will be proud of a remarkable life, lived to the full in the selfless dedication to public service".
The former Labour MP Terry Walker, who held the Kingswood seat between 1974 to 1979, said: "Jack made a considerable contribution to the life of Kingswood and the surrounding area and he will be remembered with affection."
The former Conservative MP Jack Aspinwall has died aged 82, his family have confirmed.