Sir Jeffrey yesterday spoke of how his father was “seriously ill”.
Party Chairman Danny Kennedy said: “On behalf of the Ulster Unionist Party I would like to extend sincere sympathies to Sir Jeffrey and the entire Donaldson family circle on the death of a much loved husband, father and grandfather.
“Our thoughts and prayers are with them all at this sad and difficult time.”
Lagan Valley MLA and UUP Assembly Chief Whip Robbie Butler said: “I would like to send my condolences to Sir Jeffrey and his family.
“I know that the whole of Lagan Valley is thinking of them and hope that this will be of some comfort and strength both now and in the days ahead.”
Yesterday on the BBC Sir Jeffrey said he supported calls for cemeteries to reopen across Northern Ireland on a “controlled basis”.
“Having a funeral in this country, having a wake for example is a very important part of the grieving process for most people,” he said.
“It’s not just our family, it’s the wider local community that are impacted,” he said, revealing how his family had tried to communicate with his father through a window up until recently.
“I just ask that people think about the families that have lost loved ones in recent weeks... who probably feel isolated right now.”
During an interview today First Minister Arlene Foster also paid tribute to Mr Donaldson.
She said: “He was a big character in the kingdom of Mourne and someone who served his country with distinction.
“I know he was incredibly proud of his family and they were so important to him.”
On Twitter DUP Education Minister Peter Weir said: “I am very sorry to hear of the death after a long illness of Jim Donaldson. father of Sir Jeffrey.
“A family death is incredibly difficult at any time, but even more so at the moment. My thoughts and prayers are with the Donaldson family.”
A post on Funeral Times said he died peacefully at his home today.
He will be deeply missed by his wife Annie, children Jeffrey, Diane, James, Elaine, Andrew, Kingsley, Julie-Anne and Glen, and wider family circle.
He is also described as a “much loved Grandfather, Great Grandfather and Brother”.