Islam on Tuesday said The Sunday Times and The Sun had promised not to repeat the allegation and agreed to pay his legal costs and "substantial damages".
"It seems to be the easiest thing in the world these days to make scurrilous accusations against Muslims, and in my case it directly impacts on my relief work and damages my reputation as an artist," he said.
"The harm done is often difficult to repair. However, I am delighted by the settlement, which helps vindicate my character and good name."
The Sunday Times and The Sun both confirmed they were making payments to Islam but declined to specify the amounts.
"There is an agreed settlement," said Richard Caseby, managing editor of The Sunday Times. "The Sunday Times always denied liability and we disagreed with Cat Stevens' lawyers interpretation of the article, but we took a pragmatic view of the case."
Janet Anderson, a spokeswoman for The Sun, said Islam's statement was correct but declined to comment further.
"It seems to be the easiest thing in the world these days to make scurrilous accusations against Muslims, and in my case it directly impacts on my relief work and damages my reputation as an artist"
The stories appeared in the newspapers in October. The Sunday Times ran a correction in November saying it had not intended to suggest Islam supported terrorism.
"We wish to make it clear that he is not and never has been involved in any such activities and we accept that he abhors all forms of terrorism," it said.
The Sun also ran a correction.
Islam was removed from a London-to-Washington flight in September because American officials suspected him of links to terrorists, a charge he vehemently denies.
He said the US government has still not told him what the accusation was based on.
Islam said he planned to use the money from the newspapers for aid projects he started to help children orphaned by the recent tsunami in Asia.