Administrators from accountants Deloitte said restructuring firm Gordon Brothers Europe had purchased the company for an undisclosed sum.
Blockbuster collapsed in January amid competition from internet firms and the digital streaming of movies and games.
At the time, about 200 of the firm's 528 stores were closed. The supermarket Morrisons bought 49 stores from the DVD rental chain, which had 4,190 employees.
Joint administrator Lee Manning said: "Having identified a profitable core portfolio of stores we are pleased to have achieved this sale for creditors.
"Together with the previously announced store sales, more than half of the original estate has been secured for ongoing use.
"This transaction provides Blockbuster a future in the UK and we owe a special vote of thanks to all the company's employees, suppliers and customers for helping us rescue the business."
