SAN FRANCISCO — A federal judge has signed off on a $1.2 billion deal to settle the last of the consumer claims against Volks­wagen AG over its diesel emissions scandal.

U.S. District Judge Charles Breyer on Thursday approved the agreement, which settles claims by consumers and the Federal Trade Commission over nearly 90,000 3.0-liter diesel engine vehicles. Also on Thursday, Breyer approved related deals that VW reached with the U.S. Environmental Protection Agency and the California Air Resources Board as well as a $327.5 million settlement between consumers and Robert Bosch GmbH, which provided components for both the 2.0-liter and 3.0 diesel cars. Breyer previously signed off on a similar $14.7 billion settlement to resolve consumer claims involving 475,000 2.0-liter diesel vehicles in October.

Breyer approved the settlements from the bench at the end of a nearly three-hour hearing Thursday morning where four objectors raised concerns. One aspect targeted by objectors is that, unlike the earlier deal involving the 2.0-liter vehicles, owners of 3.0-liter vehicles have no option to sell their vehicles back to VW. Despite the objections, Breyer said that he found the deals “fair, adequate and reasonable” and that he would lay out his reasoning in a written order that will be issued in the coming week.