Under the new owners, the business will operate independently under a different brand, the Swiss insurer said.
"The transaction will allow the new company to retain a professional team with accumulated insurance expertise and to continue serving the Russian market," it said.
The sale is subject to approval of the relevant regulatory authorities, the company added. It didn't provide financial details of the sale.
Zurich said in March that it wouldn't take on new domestic customers in Russia and would suspend renewing existing local business.
The company said its operations in Russia are in property and casualty insurance, with about 0.3% of the country's nonlife insurance market, and mainly serving international customers in Russia.
In 2021, it had gross written premiums there of around $34 million, compared with P&C premiums of $40.12 billion for the company as a whole.