LOS ANGELES — Zurich Financial Services AG agreed to a $1.9 billion deal to acquire the U.S. car insurance unit of American International Group Inc. (AIG), which includes 21st Century Insurance Co.

Under the agreement, 21st Century Insurance will be sold to Farmers Group Inc., a Los Angeles-based subsidiary of Zurich. The deal makes Zurich, a worldwide insurance-based financial services provider, the third-largest U.S. personal line insurer.

Farmers is a multi-lines U.S. insurer of autos, homes, businesses, specialty products, life insurance and financial services, providing insurance to 10.5 million households nationwide.

21st Century, which includes the former AIG Direct business and Agency Auto business, is the third largest traditional direct writer of insurance in the U.S., and operates in 49 states and Washington, D.C. 21st Century has more than 2.4 million customers and insures more than 4 million vehicles across the country.

Ratings firm A.M. Best Co. said Zurich will benefit from the acquisition through fees generated by Farmers, and growing its market share.

“The group is indirectly strengthening its position in the U.S. personal lines market, and more particularly the rapidly growing direct lines sector, which fits with Zurich’s long term strategy to develop its partnership with the Farmers Exchanges in the U.S. personal lines market,” said the ratings firm.