General Electric Co. said Tuesday that it has agreed to sell its European private-equity finance business to Japan's Sumitomo Mitsui Banking Corp. for about $2.2 billion, the latest step in the industrial conglomerate's retreat from banking.

Known as a sponsors unit, the business finances buyouts and other transactions for private-equity firms in Europe.

GE said it would keep its $1 billion investment in the European Senior Secured Loan Programme and European Loan Programme. The deal is expected to close in the third quarter of the year.

The Wall Street Journal had reported that the companies were nearing a deal on Monday.

The Japanese bank prevailed over other bidders, including Apollo Global Management LLC and Ares Management LP, people familiar with the matter said.

A deal comes on the heels of GE's agreement to sell its vehicle-fleet financing businesses in the U.S., Mexico, Australia and New Zealand for $6.9 billion and a separate deal for its European fleet business, both announced Monday.

GE is shedding a large portion of its GE Capital business's $500 billion in assets.

Earlier in June it agreed to sell its U.S. private-equity-lending unit to Canada's largest pension plan in a deal valued at $12 billion.

SMBC has been keen on buying some of GE's assets, including its Japanese finance unit and U.S. railcar-leasing business, people familiar with the matter have said.

SMBC also is no stranger to the European leveraged-finance business, having entering the market in 1997, according to its website.

The bank's European unit has around $1.9 billion of outstanding commitments, having provided loans to buyout and other transactions, its website says.

GE's withdrawal from banking comes after investors urged the company to return to its industrial roots as market conditions and federal regulations weighed on returns.

Separately, GE said Tuesday that it won't close the sale of its appliances business to Electrolux AB in the second quarter of the year as it is still waiting for clearance from the Justice Department. GE said it hopes to close the deal by the end of the year and expects an after-tax gain of 5 cents to 7 cents a share at closing.

Write to Gillian Tan at gillian.tan@wsj.com, Ted Mann at ted.mann@wsj.com and Chelsey Dulaney at Chelsey.Dulaney@wsj.com

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