The proposal accepted by Shire's board came in late yesterday, and comprises £27.26 in new Takeda shares, and £21.75 in cash.
Takeda's fourth proposal is 53 percent higher than Shire's share price before the first offer on March 28. So far, Takeda has made three unsuccessful offers to Shire.
Peter Feldinger, who worked at Nycomed and Takeda before becoming a consultant, said the union of the two companies had stalled until Weber took charge.
The company noted that its board has agreed to extend the deadline of concluding ongoing talks with Takeda till 8 May 2018.
Shire plc, a biotechnology company, researches, develops, licenses, manufactures, markets, distributes, and sells specialist medicines for people with rare diseases and other specialized conditions worldwide.
The company also expects to get a balanced geographic footprint, enhanced financial strength and a modality-diverse pipeline through the merger with Shire.
"Shire shareholders would give their right arms to be in Sky's position - two strong U.S. firms chasing it".
At the time, Takeda said that the acquisition would strengthen its core therapeutic areas of oncology, gastroenterology and neuroscience, and balance Takeda's geographic focus to align with market opportunities in the US.
Shire brings a bench of rare-disease drugs, including for hemophilia and hereditary angiodema, that will catapult Takeda into a higher league. The combined firm would be the eighth-biggest drug maker in the world.
Earlier today, Shire said it has received a fifth takeover proposal from Takeda.
Hasegawa was determined to look overseas for growth as well as leadership.
In the pharmaceutical sector, GlaxoSmithKline shares lost 3.6 percent. With huge pricing pressures and slashing of prices on blockbuster drugs, Japan runs the risk of multinational companies redirecting their investment in drug development elsewhere.
Sky shares were the top performers of the session after USA media group Comcast submitted a 22 billion pound ($30.7 billion) bid, prompting the European pay TV group to drop its support for a lower offer from Rupert Murdoch's Twenty-First Century Fox.
In response, Twenty First Century Fox said it remains committed to its cash offer for Sky and is now considering its options.
Investors in Shire, meanwhile, have adopted a cautious stance.
The split comes amid pressure from Whitbread's two largest shareholders - USA hedge funds Elliott Advisors and Sachem Head, both of which pushed for significant changes at the London-listed group.