Under the deal, a joint venture between funds managed by the two companies will pay Extended Stay shareholders a total of $20.50 per share, up from a previous offer of $19.50 per share in March.
"The $20.50 per paired share consideration represents the Blackstone/Starwood Capital joint venture's best and final offer," the companies said in a statement.
The new bid comes a week after ISS said the deal terms of the previous $6 billion offer did not appear to be sufficiently compelling.
The amended deal has been unanimously approved by the board of Extended Stay America. The deal is expected to close on June 16, the company said.
Extended Stay specializes in economical temporary housing for healthcare professionals, and last year proved stronger than its peers even as bookings plunged across the U.S. hotel industry due to the pandemic.
Shares of Extended Stay, which owns and operates 650 hotels in the United States, were up about 1% before the bell.
(Reporting by Sanjana Shivdas in Bengaluru; Editing by Devika Syamnath and Krishna Chandra Eluri)