Insurance Commissioner Steve Poizner announced Friday that he has approved the sale of Woodland Hills-based 21st Century Insurance to Farmers Group Inc.

Farmers, the Los Angeles subsidiary of Swiss insurance conglomerate Zurich Financial Services Group, had announced plans April 16 to acquire AIG’s personal auto insurance group, which includes 21st Century.

The $1.9 billion deal, expected to become effective July 1, will make Farmers Group the nation’s third-largest personal lines insurer.

AIG has been seeking to sell portions of its business, including Los Angeles aircraft leasing company International Lease Finance Corp., to repay $100 billion in government aid the company has received in recent months.