The deal with the Weiss family, who made their initial offer six months ago, is valued at about $878m (£576m) including debt and settlement of stock options.
Shareholders excluding the family and related entities will receive $18.20 per share in cash, plus an additional 15-cent dividend if the deal closes in July as planned.
Excluding debt and including the dividend, the deal values American Greetings at about $580m.
American Greetings, whose traditional competitor is privately-held Hallmark Cards, said a special committee of independent directors had concluded that the deal with was fair and in the best interests of shareholders.
The Weiss family and affiliates control more than 50 per cent of the Cleveland, Ohio-based company’s voting shares.
The firm, which describes itself as the world’s largest publicly owned creator, manufacturer and distributor of social expression products, went public in 1958, about 52 years after it was founded by Polish immigrant Jacob Sapirstein.
More recently, it has been hurt by costs related to the bankruptcy of its UK distributor, Clinton Cards, last June. Clinton Cards failed to repay a £35m loan to American Greetings.
The firm reported a loss of $809,000 in the third quarter ended 23 November, compared with a year-earlier profit of $20.2m.
Revenue rose to $507m from $465m, but about $68m of revenue in the latest quarter came from the takeover of about 400 Clinton Cards’ stores in the UK.