Those detained at the controversial US-run camp and the UK government were bound by confidentiality agreements about the payments, which were reported to run into millions of pounds.
Making a Commons statement yesterday, Mr Clarke said: "The government has now agreed a mediated settlement of the civil damages claims brought by detainees held at Guantanamo Bay. The details of that settlement have been made subject to a legally-binding confidentiality agreement."
He added: "No admissions of culpability have been made in settling these cases nor have any of the claimants withdrawn their allegations."
Settling the High Court actions will pave the way for a judge-led inquiry into allegations that British security and intelligence services were complicit in torture.
Shadow justice secretary Sadiq Khan asked for details of the cost of the payments, claiming there was a "public interest in knowing the total sums involved in this settlement".
But Mr Clarke told him the settlement "could be reopened if either side started breaking the confidentiality" agreement, but said there was a "gain" from mediating the claims instead of mounting a lengthy court battle.
Earlier this year Prime Minister David Cameron announced that an inquiry into the allegations - led by Sir Peter Gibson - would be held once the civil cases and a police investigation had concluded.
• Analysis: Better legal advice needed to avoid a repeat showing
Mr Clarke said yesterday: "The Prime Minister has repeatedly made clear that this coalition government is unswerving in its opposition to torture or the ill-treatment of prisoners or detainees. We do not condone it, nor do we ask others to do it on our behalf."
Announcing the settlements to the Commons, Mr Clarke said the National Audit Office and Sir Malcolm Rifkind, the Conservative MP who is the current chairman of the Intelligence and Security Committee, had been given details of the payments in confidence.
Mr Clarke said: "The alternative to any payments made would have been protracted and extremely expensive litigation in an uncertain legal environment in which the government could not be certain that it would be able to defend departments and the security and intelligence agencies without compromising national security.
"The cost was estimated at approximately 30 million to 50m over three to five years of litigation.In our view there could have been no Gibson Inquiry until that litigation had been resolved."
The settlement was a "significant step forward" in resolving the issues, he added, and was supported by the heads of MI5 and MI6.
A government green paper will be published next summer examining how sensitive information is treated in courts and inquiries, Mr Clarke added.
Claims have been settled with 16 former detainees, including 12 cases that were before the courts and a further four who would have come before the courts.