Sami al-Saadi, a leading Gaddafi opponent, was imprisoned and tortured after he was forced to board a plane in Hong Kong back to Tripoli, along with his wife and four children in 2004.
The rendition was part of joint UK-US-Libyan operation.
Ministers are now understood to have offered him a sum of £2.2m, but the government has not admitted liability, Mr al-Saadi said.
“My family suffered enough when they were kidnapped and flown to Gaddafi’s Libya,” he said.
“They will now have the chance to complete their education in the new, free Libya. I will be able to afford the medical care I need because of the injuries I suffered in prison.”
‘As bad as the torture’
But he said that he was unlikely to get the answers he was looking for.
“I started this process believing that a British trial would get to the truth in my case. But today, with the government trying to push through secret courts, I feel that to proceed is not best for my family.
“I went through a secret trial once before, in Gaddafi’s Libya. In many ways, it was as bad as the torture. It is not an experience I care to repeat.
“Even now, the British government has never given an answer to the simple question: ‘Were you involved in the kidnap of me, my wife and my children?’
I think the payment speaks for itselfSami al-Saadi
“I think the payment speaks for itself. We will be donating a portion of the proceeds to support other Libyan torture victims.
“We look forward to the result of the police investigation and hope there will be a full and fair public inquiry into our case.”
A Foreign Office spokesman said: “We can confirm that the government and the other defendants have reached a settlement with the claimants.
“There has been no admission of liability and no finding by any court of liability.”