Zimmer will pay $10.35bn in cash and issue $3bn worth of shares to Biomet shareholders, which include Goldman Sachs Capital Partners, KKR, Blackstone and TPG Capital.
The private equity firms took the company private in an $11.4bn deal in 2007.
Last month the company filed for an IPO and it was reported at that time that it could raise more than $1bn.
It reportedly hired Bank of America Merrill Lynch, Goldman Sachs and JPMorgan Chase to manage the share sale.
In 2012 Biomet paid $22m in charges to settle allegations that it bribed doctors in Argentina, Brazil, and China for nearly a decade.
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