The FTC said the software "exposed consumers to significant security risks and was unreasonably difficult to uninstall".
Under the settlement, Sony BMG must allow consumers to exchange affected CDs bought before 31 December 2006, and reimburse them up to $150 (£76) to repair damage to their computers.
Consent
Sony BMG, which agreed to the settlement figure, did not admit a law violation and the FTC will decide whether to make the settlement final after a 30-day public consultation.
In 2005, the company shipped more than 12 million CDs, each loaded with one of two anti-piracy programs.
About seven million of the CDs were sold and the Digital Rights Management software installed itself on consumers' computers without their knowledge or consent.
CDs by artists such as The Coral, Alicia Keys, Dido, the Foo Fighters and the Backstreet Boys were among the affected discs.
No-one from New York-based Sony BMG was available for comment.
In December, the company settled similar cases with more than 40 states, agreeing to pay more than $4m (£2.03m) to reimburse customers.