The share offer, which marks a premium of 36 percent over Baxalta's stock price on August 3, would give the U.S. firm's shareholders about 37 percent of the combined group.
Shire's Chief Executive Flemming Ornskov said he had gone public with its plan, which it first proposed privately last month, after Baxalta's board declined to engage in substantive discussions.
"We believe the proposed combination of Shire and Baxalta would be strategically and financially attractive for both of our companies, accelerating our respective growth ambitions and creating the leading global biotech company in rare diseases," he said.
"It is our strong preference to immediately enter into a negotiated transaction to explore the full potential of the proposed combination and finalise the terms of an agreement."
Shares in Shire were down 4.7 percent on the news.
(Reporting by Paul Sandle; additional reporting by Ankur Banerjee; editing by Kate Holton)
