Bed Bath & Beyond Inc. said it would add three new directors and explore options for its buybuy Baby business as part of an agreement with activist investor Ryan Cohen.

The agreement announced Friday comes after Mr. Cohen sent a letter to the company criticizing the retailer’s turnaround strategy and calling for a separation of the buybuy Baby chain or a sale of the entire company. Mr. Cohen’s firm, RC Ventures LLC, owns a roughly 9.8% stake in Bed Bath & Beyond.