Mr Adam was first elected to Holyrood in 1999 as a regional MSP for the North East, and from 2003 as a constituency MSP for Aberdeen.
He also served as SNP chief whip from 2007 to 2011, and as the minister for Parliamentary Business from May 2011 until September last year.
Speaking at First Minister’s Questions, Alex Salmond said: “Brian was an exceptional MSP and was one of the crucial people who as chief whip sustained the minority government between 2007-2011. I was delighted to see him serve as a minister in this Parliament.
“Of course, his greatest service was to the people of Aberdeen for a quarter of a century - first as a councillor and then as an MSP.
“I’m proud to say I’ve known and admired him over that entire period as an outstanding politician, a fine human being and a dear friend.
“My condolences go to Brian’s wife Dorothy and his five children - Neil, Jamie, Sarah, David, Alan - and the wider family at this very difficult time.”
Holyrood’s Presiding Officer Tricia Marwick said the Parliament’s flags were flying at half mast for Mr Adam.
She said a book of condolence would be available for members to sign while there would be an opportunity to pay full tribute to him during parliamentary debating time next week.
A statement from Mr Adam’s family said: “Brian had a hard-fought battle with cancer, but passed away peacefully during the night at home.
“We would like to thank Brian’s colleagues and constituents for their huge support over this challenging and sensitive period.
“The immediate family have all been informed of Brian’s passing and the funeral arrangements will be announced in the next few days.
“Until then we would be grateful if the press would respect our family’s privacy at this difficult time.”
Mr Adam was born in Newmill, Banffshire, and educated in the north east at Keith Grammar School. He studied at Aberdeen University and worked with Glaxo in Montrose and at Aberdeen Royal Infirmary as a biochemist.
He began his political career at Aberdeen District Council in 1988, becoming an Aberdeen City councillor in 1995.
Politicians from across the political spectrum paid tribute to Mr Adam.
Dame Anne Begg, Labour MP for Aberdeen South, said: “Brian always worked hard for his constituents and continued to do so despite his obvious illness.
“Brian has been a key figure in the Aberdeen political scene for a very long time and will be sorely missed. My thoughts are with his family at this sad time.”
Labour leader Johann Lamont said: “I have always recognised (Mr Adam) as a man of strong conviction, of decency, of profound faith. A man who cared deeply for his family, his party and his country.
“Our thoughts are with those who feel his loss most sorely. I know this is a sad day indeed for those here who not only had the privilege of working with him as a colleague, but love him as a friend.”
Conservative leader Ruth Davidson echoed Ms Lamont’s comments. She said Mr Adam had served with “diligence and decency”, and that the thoughts of Tory MSPs were with his family, friends and colleagues.
Scottish Liberal Democrat leader Willie Rennie said: “We are all deeply saddened at the passing of Brian Adam, who served the parliament, his party and his community well.
“A compassionate and decent man, he will be dearly missed at Parliament. My thoughts are with his family and his colleagues at this difficult time.”
Mr Adam’s death will trigger a by-election in the Aberdeen Donside constituency. He won the seat with 55 per cent of the vote in the 2011 elections.