In a statement issued by his solicitors, Mr al-Saadi said he was settling because his family had "suffered enough".
Referring to why he had accepted a pay-out, he said: "[My children] 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.
"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?"
In a statement, a spokesman for the Foreign Office 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."
www.bbc.co.uk/news/uk-20715507