The agreed cash-and-share offer was an improvement on a previous bid of USD 30 billion that Baxalta had rejected in August. The transaction is expected to be completed in mid-2016, Shire added in a statement.
The purchase of the Deerfield, Illinois-based group will boost Shire's position in the market for rare-disease treatments in the pharmaceutical sector, which is undergoing rapid consolidation.
Following the deal, Baxalta will benefit from lower taxation because Shire is based in Ireland -- which boasts ultra-low corporation tax.
"Our expanded portfolio and presence in more than 100 countries will drive our growth to over USD 20 billion in anticipated annual revenues by 2020."
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The offer values Baxalta at the equivalent of USD 45.57 per share, which marked a premium of 37.5 per cent above the share price on August 3. That was one day before Shire confirmed its interest in Baxalta.
London-listed Shire forecasts that it will generate more than USD 500 million in annual cost synergies within three years of the closing of the transaction.
Faced with expiring patents and growing competition from generics, pharmaceutical firms like Shire increasingly view so-called orphan drugs -- which target rare diseases -- as a path to growth.
The latest deal meanwhile "presents a unique opportunity for Baxalta shareholders, who will receive substantial immediate value as well as an ongoing stake in a combined global leader in rare diseases with strong growth prospects", added Baxalta chief executive Ludwig Hantson.
"We bring to Shire a strong portfolio and pipeline of market-leading products, high-quality manufacturing capabilities and a talented global workforce that places patients at the center of everything we do."