He made 65 appearances in all competitions for the Northumbrians, managed by ex-Raith and Falkirk midfielder Paul Smith and playing in the Scottish Second Division at that time, before heading back north in 2005 to join East Fife and staying there also for two seasons.
Hampshire also played for Dunbar United, his home-town club, from 2008 to 2009 and Newquay in Cornwall after that.
Rangers vice-chairman Craig Forsyth, a member of their board of directors during Hampshire’s stint there, paid tribute to him, saying: “We were incredibly saddened to learn about Paul’s passing.
“Paul was a fantastic, technically gifted footballer – the sort fans would pay their admission money alone to watch – and was a great asset to the club in his two seasons, particularly in the 2003/04 season, when he only missed one league match.
“He was also a top professional and a great person to be around, and all at the club would like to send our condolences to Paul’s family at this sad time.”
Hampshire’s senior career started at Raith Rovers in 1998 and a spokesperson for the Kirkcaldy club added: “We were saddened to learn of the passing of former player Paul Hampshire, who died after being struck by a car on Sunday.
“Paul signed for Rovers on the same day as Laurie Ellis in July 1998 from Hutchison Vale and went on to make 69 appearances, scoring two goals.
“A native of Dunbar, he was the younger brother of Steven, a striker who played for Chelsea and Dunfermline Athletic.
“Paul is remembered as being blessed with a wonderful left foot, and he left Rovers to sign for Berwick Rangers in May 2003.
“He also played for East Fife before playing out the remainder of his career in junior football.
“Our thoughts are with the Hampshire family.”