SHANGHAI, May 6 (Reuters) - The China venture of U.S. life insurer Metlife Inc has become the first foreign-backed insurance firm to receive regulatory approval to set up a branch in Shanghai's free trade zone.

The approval was announced by Sino-US United Metlife Insurance Co Ltd, jointly operated by state-owned Shanghai Lianhe Investment Co and Metlife, on its official microblog on Monday.

The move comes nearly eight months after the free trade zone was launched, receiving considerable attention from overseas firms and hailed as potentially one of China's boldest reforms in decades. However, that hype has cooled amid a lack of specific policy details since the initial fanfare.

Foreign banks, such as Citigroup Inc < and HSBC Holdings PLC, have set up branches in the free trade zone but many foreign companies have been reluctant to follow suit citing a lack of clarity over what they exactly will be allowed to do in the zone.

The China Insurance Regulatory Commission has said insurance firms will be allowed to enjoy looser restrictions on offshore investment and yuan-dominated cross-border reinsurance businesses compared with operations on the mainland, although no details have been published so far.

Foreign insurers are only allowed to operate in China, including the free trade zone, through joint ventures with local partners.

(Reporting By Shanghai Newsroom; Editing by Kazunori Takada and Kenneth Maxwell)