Shire shareholders will end up owning 25 percent of the new merged group.
AbbVie said it expects the deal will cut its effective tax rate to approximately 13 percent.
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Shire shares were up as much as 2.5 percent shortly after the deal was announced.
If the takeover is successful, North Chicago-based AbbVie plans to relocate the new combined firm in the U.K., allowing it to benefit from the country's lower tax.
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Shire is the second FTSE-listed pharmaceutical firm that has been approached by a U.S. rival, after Pfizer's failed takeover bid for U.K. group Astra Zeneca.
The Shire Board, has been advised by Citi, Deutsche Bank, Evercore, Goldman Sachs and Morgan Stanley. Shire said the banks consider the terms of the transaction to be fair and reasonable.
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