WASHINGTON—Three drug makers agreed Tuesday to pay $421 million to settle U.S. claims that they bilked federal health-care programs out of millions by greatly inflating the price of their drugs.

According to the Justice Department, Abbott Laboratories Inc., Roxane Laboratories Inc. and B. Braun Medical Inc. reported false prices to the government to get larger Medicare or Medicaid reimbursements for the doctors and pharmacists choosing their drugs.

The...