Steinway, which has been in business for 160 years, said previously that it was looking into selling the company.
Kohlberg, which would take the company private, will start a tender offer to buy all of Steinway's outstanding stock for $35 per share, a 15 percent premium to its Friday closing price of $30.43.
The board of the Waltham, Mass., company unanimously recommended Monday that shareholders tender their stock.
The deal includes a 45-day "go-shop" period in which Steinway may seek out alternative bids.
Steinway & Sons was founded in 1853 in a loft on Manhattan's lower west side. Its products include Bach Stradivarius trumpets, Selmer Paris saxophones, C.G. Conn French horns, Leblanc clarinets, King trombones, Ludwig snare drums and Steinway & Sons pianos.
"Kohlberg's long history of collaboration to grow and expand some of the world's leading consumer brands makes us an ideal partner for Steinway to accelerate its global expansion, while ensuring the artisanal manufacturing processes that make the company's products unique are preserved, celebrated and treasured," Kohlberg partner Christopher Anderson said.
Shares of Steinway Musical Instruments Inc. jumped $4.62, or 15 percent, to $35.05 in morning trading. Shares this year have risen close to 70 percent.
The transaction is expected to close in the third quarter.