The star of BBC show Coast deleted his Twitter account after being being bombarded with hate-filled messages after he spoke out in favour of the Union.
Internet trolls sent him messages saying they hoped he got cancer cancer and said he was a traitor who deserved to be burnt alive.
The historian and archaeologist had more than 40,000 followers on the social networking site but has now closed it down after growing tired of the abuse.
He said: “A great chunk of the response was not just negative but very personal and filled with bile and vicious loathing.
“People made it clear they wished the worst for me. They wished that I would develop cancer and said I deserved to be burnt as a traitor. It was one or two positive comments accompanied by hundreds of hate-fuelled messages.
“It just got to the point where I was getting so much abuse that I woke up one day and thought, ‘Why am I bothering having this intrusion in my normal life?’
“I realised that by having a Twitter identity I had opened a door into my personal life in which strangers could pass at will. The minute I deactivated my account I felt like I had brought my head out of deep water and could breathe easily. It was an almost instantaneous fix.”
He added: “Forty thousand Twitter followers was a sacrifice worth paying.
“I experimented with social media without realising what the consequences would be.”
Mr Oliver, who was born in Renfrewshire, wrote an article in May in which he referred to the independence referendum as a “hate fest” and castigated first minister Nicola Sturgeon for leaving the door open on a future vote on the issue.
He also described Alex Salmond as a “round, wrecking ball of a man” and called the prospect of a second referendum a “cancerous presence”.
The 49-year-old, who presented BBC series A History Of Scotland, said he worried about the effect of social media on his three young children.
He said: “In the old days if you wanted to tell the prime minister that you disagreed with him or her, you’d have to write a letter to Downing Street.
“But now, on a whim, you can instantly wish death and damnation on a total stranger. I know there are people who thrive on the confrontational aspect of it. But I don’t like it, to me social media is bad news.
“It bothers me that when my wee girl comes home from school she can’t leave school behind in the way that I did.
“Now school follows children around and is pinging by their beds as they try to get to sleep. I knew the stress social media was causing me was different because I can remember a time without it. But for kids that have grown up knowing nothing else, they can be under stress — but have no way of knowing it.”
Earlier this month David Torrance, the broadcaster and political author, left Twitter, claiming that he could no longer cope with the abuse he was receiving from so-called cybernats.