The family had also charged Adams County employees ignored evidence the children had been sexually abused in a foster home, The Denver Post reported Thursday.
The money will be divided into trusts for each child that will be administered by a court-appointed conservator.
In agreeing to the settlement, believed to be the largest of its kind in Colorado, Adams County did not admit any wrongdoing, the newspaper said.
County Attorney Heidi Miller said the money was paid because the family was "claiming damages in the millions."
No changes in county procedures are required by the settlement.