NEW YORK — General ­Electric has agreed to sell a commercial property lender to ­EverBank Financial for $2.51 billion in cash, as chief executive Jeffrey Immelt shrinks GE’s real estate operations.

The deal for Business Property Lending includes $2.44 billion in performing commercial real estate debt and servicing rights on $3.1 billion of loans securitized by GE Capital, the companies said Monday. The sale is expected to close next quarter.

Immelt has been working to get out of some businesses tied to real estate as he pares GE ­Capital’s balance sheet after $32 billion of credit losses during the financial crisis.

The acquisition will immediately provide a ‘‘low double- digit’’ boost to earnings per share, said ­EverBank.

The sale will reduce by $5 billion GE Capital’s ending net investment, a measure of the unit’s size that excludes cash and liabilities that do not bear interest, a spokesman said.

GE Capital sold its Irish mortgage unit last month to Pepper Home Loans Group, Australia’s largest nonbank mortgage lender.