The business, which includes outstanding loans of about $1.4 billion, provides real estate financing to owners of limited service hotels.
GE said it would also sell to an unnamed buyer its business that provides financing to Canada's hospitality and restaurant industries. The unit has about $300 million of loans.
GE said it would gain about $200 million from the deals, which are expected to close in the second quarter.
Both the businesses represent a large part of GE Capital's franchise finance unit, which is the last North American business to be sold as part of a plan to cut down the size of GE Capital, GE said.
The deal is expected to immediately add to Western Alliance's earnings, the bank said in a separate statement.
Reporting by Ramkumar Iyer in Bengaluru