Mr Weir and wife Chris, from Largs in North Ayrshire, claimed the £161m prize in July 2011.
The Weirs, who confirmed earlier this year they were to divorce, made a donation of £1m to the Scottish independence campaign ahead of the 2014 referendum – and continued donating to the SNP afterwards.
Scotland’s First Minister Nicola Sturgeon said she was “incredibly sad” to hear of the death.
She said: “Colin’s determination and generosity in the cause of Scottish independence cannot be overstated and was hugely appreciated. The SNP and the independence movement has lost a true friend today and we will miss him dearly.”
The former TV cameraman and his then-wife, a former psychiatric nurse, made The Sunday Times rich list with the huge lottery win eight years ago.
In 2013 the Weirs set up The Weir Charitable Trust and made a donation to a community football club in Largs.
They also invested in Partick Thistle football club which led to the youth set-up being rebranded the Thistle Weir Youth Academy and a section of their Firhill Stadium being named the Colin Weir Stand.
In November of this year Mr Weir secured a majority shareholding at the club and promised to give the 55 per cent shareholding directly to a fans’ group by March 2020.
The club tweeted: “On behalf of everyone at Partick Thistle, our love, thoughts and prayers are with the family and close friends of Colin at this most difficult time.”
SNP MSP Mike Russell, one the Scottish government’s cabinet ministers, also paid tribute.
He said: “Sad to see this – remember him very kindly, both of us contesting seats in 1987, working on PPBs for the SNP when I was VC Publicity & his great generosity after his win.”
Their £161m prize was the UK’s biggest win until October this year, when an anonymous ticket holder claimed a £170 million jackpot.
News of the intention to divorce after 28 years of marriage broke in April this year, with reports indicating it had been granted in September.
A spokeswoman for Mr Weir’s personal lawyers said: “It is with deep sadness that we announce the passing of Colin Weir early today after a short illness.
“We would ask for privacy for his family and friends at this distressing time. No further comment will be made other than to offer sincere thanks to the staff of University Hospital Ayr for their care and compassion.”