The debt to Swiss-based financial company Langston, of whom former Bluebirds chief Sam Hammam is a representative, was taken out in 2004 and was believed to be worth £24million.
Cardiff's most recent financial figures showed the club were £83million in debt.
Cardiff owner Vincent Tan had stated he was confident of reaching an agreement after holding talks with Hammam, and a deal has now been struck.
It is believed Cardiff agreed to pay a one-off lump sum and a schedule of further, smaller payments.
Tan said: "I am grateful and indebted to Sam Hammam, Michael Isaac and Michael Filiou for their part in this resolution, which brings to a close a lengthy period of uncertainty.
"This settlement allows us to look to a new era of financial stability, which should be celebrated by all connected to Cardiff City.
"I am delighted, primarily for the supporters of this great club that we can put this matter firmly behind us and plan for our future with confidence."
Hammam will become an honorary life president of the club, while his representative Filiou has taken a place on the board.
"This resolution will rightly be regarded as a proud and historic occasion for all associated with Cardiff City Football Club," said Hammam.
- Sam Hammam