The broadcaster and writer won the WH Smith Literary Award 2000 for his acclaimed book The Soldier's Return, which is published next week.
Literary giants shortlisted for the award included J M Coetzee for his book Disgrace which won him the Commonwealth Writer's prize and the Booker Prize for the second time.
Receiving the award on Thursday, Lord Bragg said he wished his father had been alive to witness it.
"I'm very surprised," he said. "I was surprised to even be on the shortlist.".
"More than that I'm delighted. If I'd known I was going to win I would have had one less glass of red wine."
A 'masterpiece'
The South Bank Show presenter, who published his first novel, For Want of a Nail, in 1965, said the new book was triggered by the death of his father.
"Like millions in this country he spent six years of his young life abroad then came back to find a young child, in my case nearly seven, who had grown," he said.
"That's the novel I wrote and I wish he was here today," he added.
Author Beryl Bainbridge won the award last year for her book Master Georgie.
Professor John Carey, chair of the judging panel, said Lord Bragg's work drew on personal memories but raised common problems - family breakdown, fatherhood and the nature of masculinity.
"This restrained but compelling novel is both an intimate social documentary and a moving human story," he said.
"After a lengthy judging session The Soldier's Return, in our view Melvyn Bragg's masterpiece, triumphed over its rivals in a formidably strong shortlist."
Other authors shortlisted for W H Smith's 42nd prize literary award were Joanna Bourke for An Intimate History of Killing, Howard Jacobson for The Mighty Walzer, Francis Wheen for Karl Marx and Ann Wroe for Pilate.