The black and white feline, named after Basil Fawlty's wife in the hit 1970s comedy Fawlty Towers, was brought to London by Alistair Darling after he became Chancellor of the Exchequer in Brown's government in June 2007.
Sybil died earlier this week at the home of a family friend, a Downing Street spokesman said.
Sybil's predecessor as chief mouser in the seat of government was Humphrey, who arrived in 1989 when Margaret Thatcher was in office, but left shortly after Blair came to power.
Looking for a Personalised Pet Memorial Stone? Check out this one and a range of other pet care products at 24ace.co.uk