Mr Tinniswood was born in Liverpool on Aug 26, 1912, and died on Nov 25.
He became the world’s oldest man in April following the death of 114-year-old Venezuelan Juan Vicente Perez.
"His last day was surrounded by music and love," the family said in a statement, also thanking "all those who cared for him over the years".
Born the same year the Titanic sank and living through both world wars, Mr Tinniswood told Guinness World Records that the secret to his longevity was "pure luck".
"You either live long or you live short, and you can’t do much about it," he said.
He nonetheless advised moderation in all things to stay healthy.
"If you drink too much or you eat too much or you walk too much, if you do too much of anything, you’re going to suffer eventually," he added.
During World War II, Mr Tinniswood held an administrative role in the Royal Army Pay Corps, going on to work in accounts for oil giants Shell and BP.
He was a lifelong supporter of the Liverpool football club, and ate fish and chips every Friday.
The world’s oldest living woman currently is Japan’s Ms Tomiko Itooka, who is 116.