Ohio-based American Greetings, which has been one of Clinton's biggest suppliers, will take on the brands and assets of the retailer.
The group, which was the UK's largest specialist cards retailer and operated 628 Clintons and 139 Birthdays stores, collapsed into administration in early May.
An estimated 397 stores are expected to be saved in the deal with the US firm, which generates revenues of around £1bn annually.
Zolfo Cooper, the administrator, has already announced the closure of around 350 stores, costing the jobs of nearly 3,000 full and part-time staff.
American Greetings placed itself in pole position to buy the chain after it snapped up Clinton's £35m bank debt, making it a preferential creditor and giving it a strong position in sale talks.
The US company's UK operation, which is based in Dewsbury, West Yorkshire, has the brands Camden Graphics, Hanson White, Forget Me Not and Xpressions.
It supplies various outlets including major supermarket chains.
The final number of stores acquired will be dependent on negotiations with landlords at each location.
Its (Euronext: ALITS.NX - news) chief executive Zev Weiss said: "We are pleased to welcome these stores, the Clinton Cards brand, and the approximately 4,500 employees as members of the American Greetings family.
"We believe that properly managed, and with the appropriate capital structure, Clinton Cards can be both an important and profitable retailer in the speciality channel of distribution over the long term."