LOS ANGELES—Zurich Financial Services Group’s Farmers Group Inc. unit has completed its acquisition of American International Group Inc.’s personal automobile insurance business, Farmers announced Wednesday.

The purchase price for AIG’s personal auto business, which includes 21st Century Insurance as well as the former AIG Direct and Agency Auto business, was approximately $1.9 billion, according to Los Angeles-based Farmers. The acquisition is the largest in Farmers’ 81-year history.

The sale is part of AIG’s effort to raise money to pay back federal government assistance.