Volvo Cars said it has agreed to supply Uber Technologies Inc. with a fleet of 24,000 self-driving taxis beginning in 2019—one of the first and biggest commercial orders for such vehicles.

The deal between Volvo, owned by China’s Zhejiang Geely Holding Group Co., and Uber was disclosed Monday as a framework agreement without financial terms. Such an order, though, would account for about 4.5% of Volvo’s current total sales, based on 2016 figures, and is estimated to be worth more than $1 billion, a person familiar with the...