Mr Cobain, a former Mayor of Belfast who was in the UUP for 31 years, said he had become "disillusioned" with the party, which he believes is in decline.
"I have thought about this for a very long time," he said.
"It is not a decision that I have taken lightly. I think have been really disillusioned with the party for a number of months. It is riven with personal and policy difficulties and I think that can only get worse into the future.
"I think the Ulster Unionist Party is a party that is best described as politically exhausted. I think they do not have any new ideas or big ideas."
Mr Cobain spent 13 years as an MLA, before losing his North Belfast seat in the 2011 election to DUP MLA Paula Hamilton.
He said the DUP represents a strong, cohesive future for unionism
"Throughout my career I have always recognised the importance of unionism working together for the benefit of everyone in the community.
"The unionist community is not well served by a fractured and divided unionism," he said.
DUP leader Peter Robinson welcomed the 66-year-old father of two to the party and said Mr Cobain's working class connections would be well used.
"As Chairman of the Social Development Committee in the last Assembly, Fred was known as a champion for those with social and economic problems.
"I know Fred will be a valuable member of the DUP and will have an important role to play in the party as we continue to move Northern Ireland forward," said Mr Robinson.
Mr Cobain is the latest high-profile defector from the UUP, following Strangford MLA David McNarry, who left last year after he was disciplined over a press interview he gave on Unionist unity.
Mr McNarry is now a UKIP MLA, and the party's only member in the Assembly.
In August, UUP peer Lord Magennis quit Mike Nesbitt's party after comments he made about gay marriage.
Last month the party whip was removed from Basil McCrea, MLA for Lagan Valley, after he said he agreed with the policy of flying the Union Flag on designated days at Belfast City Hall.