The deal, initially announced by Medtronic in July, was seen as a move by the device maker to jump-start its spinal business. Kyphon designs medical devices to treat and restore the spine in the U.S. and Europe.
Medtronic is best known for its implantable pacemakers and defibrillators, spinal implants and insulin pumps.
Directors of both companies have unanimously cleared the deal, and Kyphon shareholders signed off on it two weeks ago.
Kyphon shareholders will receive $71 (49.04 EUR) per share in cash for each share of Kyphon common stock. Medtronic put the total value of the deal, including payment of Kyphon debt, at $4.2 billion (2.9 billion EUR).
Medtronic said it financed the deal primarily with cash on hand.
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