The Labour MP for Inverclyde was taken into intensive care eight weeks ago.
Mr Cairns, 44, died at 11pm on Monday at the Royal Free Hospital in north London. He leaves behind his partner Dermot, father John and brother Billy.
Labour Party leader Ed Miliband paid tribute to Mr Cairns.
He said: "David will be missed beyond measure as a former minister, as an MP, as a friend and a colleague by many people and my heart especially goes out to his partner Dermot and his family in Scotland.
"David was an immensely talented Member of Parliament who campaigned diligently on behalf of his constituents in Greenock and Inverclyde.
"A highly effective minister of state in the Scotland Office, he was Labour through and through and yet was much-respected across the political divide.
"He was also a man with a wide hinterland. As a former Catholic priest, he brought a sensitive understanding of others and a ready wit to politics, and he never shied away from saying what he believed to be true.
"The Labour Party will miss him profoundly. He was a good man."
Former prime minister Tony Blair, who first appointed Mr Cairns as a government minister, said he was extremely saddened to hear of his untimely death.
"David's life was dedicated to public service. He was a committed and conscientious constituency MP, an excellent government minister and a passionate campaigner for social justice, equality and opportunity.
"But more than that, David was, quite simply, a good man, with time for everyone and a wonderful sense of humour, which made him a delight to be around.
"Westminster, politics and the Labour Party will be poorer without him. My thoughts and prayers are with Dermot and all David's family and friends."
Mr Cairns, a former Catholic priest, was first elected to the Westminster Parliament in 2001 as Labour MP for Greenock and Inverclyde.
He resigned from the previous Labour government in September 2008 during the fallout over Gordon Brown's leadership.
In the 2010 General Election, he was returned as Inverclyde MP with a majority of 14,416.
Scottish Labour leader Iain Gray said Mr Cairns was a man of "enormous dignity, courage and outstanding intellect" whose loss would be huge.
Mr Gray said: "I worked closely with David and the Scotland Office, and everyone who knows David will be devastated by this news, and at such a young age.
"His time as a minister was characterised by good humour, good judgment and good character. He had so much more to give his party and his country. He is a huge loss to Scottish and progressive politics.
"His shrewd political analysis never dulled his quick wit and sense of fun. His true calling in life was always to help others."
Before Mr Cairns became an MP, Parliament had to reverse a law dating back to the 19th century which banned former Catholic priests from taking up a seat.
The House of Commons (Removal of Clergy Disqualification) Act 2001 was passed to allow him to enter Parliament.
Duncan McNeil, MSP for Greenock and Inverclyde, said: "This is such a huge loss. People are just shell-shocked.
"David was a colleague and a friend to so many people, and highly-respected. He was a big talking point in Inverclyde - people were always asking how he was doing these last few weeks.
"People have handed in cards and I know prayers have been said for him across all faiths. People in Inverclyde were enormously proud to have such a talented and respected MP representing them."
Shadow Scottish secretary Ann McKechin said: "He was a dear colleague of exceptional skill, widely recognised in and out of Parliament.
"He was a good friend to us all and we will miss him enormously. Our thoughts are with his family at this most difficult of times."
Rutherglen and Hamilton West MP Tom Greatrex, who worked alongside Mr Cairns at the Scotland Office, described him as a "gifted and dedicated" politician.
Mr Greatrex said: "His energy, drive and commitment to the creative industries in Scotland will be sorely missed in Parliament.
"He was a good friend and his tragic loss at such an early age is a real blow. My thoughts are with his family and friends at this very sad time."
The death of Mr Cairns means there will be a by-election for the Inverclyde constituency.
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