Wells REIT II Inc. has purchased 333 Market St., a 657,115-square-foot office building in San Francisco's financial district that is fully leased to Wells Fargo Bank.

The Atlanta REIT, whose shares do not trade on any exchange, purchased the 33-story building from the Korean Federation of Community Credit Cooperatives, which bought it in 2010 for $333 million, or $507.76/sf. Wells Fargo leases the building through 2026. It is said to have also provided...