It lost £4.9m in 2015 and £8.4m in 2016, with analysts suggesting much of its value was attached to its prestigious name.
Tandem is a crowd-funded start-up firm which has yet to launch its bank accounts and other financial services through its money management app.
A statement from Tandem said that under the terms of the agreement, Tandem will acquire 100% of Harrods Bank and benefit from around £80m of capital coming into the business.
It noted that the financial terms had not been disclosed and on completion the bank will operate under the Tandem brand.
“The acquisition will accelerate Tandem’s launch plans to offer savings accounts to its customers, subject to regulatory approval, before the end of the year,” it added.
Credit cards are set to be launched in the next few months.
Tandem founder Ricky Knox said: “Tandem has been built from the ground-up with the help of over 11,000 co-founders, who have helped us shape products and services that really make a difference to their lives.
“This acquisition will allow us to scale the business and ensure we can introduce as many people as possible to a new way of banking.”