LONDON—Reckitt Benckiser Group PLC agreed to pay up to $1.4 billion to settle U.S. investigations into whether its former pharmaceuticals unit organized a multibillion-dollar fraud to drive up sales of an opioid-addiction treatment.

The U.K. consumer-goods company, whose products include Lysol cleaner and Durex condoms, said Thursday that it had struck a deal with the U.S. Department of Justice and the Federal Trade Commission to resolve their long-running probes into the sales and marketing of Suboxone Film. It is the biggest...