The company is now willing to pay £47 per share, of which £21 would be cash and £26 new Takeda shares.
This represents a seven per cent increase on the original proposal of £44 per share made at the end of March.
Takeda said the offer was a compelling opportunity for Shire shareholders.
"On completion of the proposed acquisition, Shire shareholders would hold a very meaningful stake in a leading global biopharmaceutical company and benefit from the material synergies expected to be derived from the acquisition," the company said in a statement.
Shire said yesterday that it had rejected Takeda's £43bn offer (along with two other bids from Takeda), but it confirmed the two were still in ongoing talks over whether a "further, more attractive" deal could be hammered out.
Yesterday it looked as if a bidding war could emerge for Shire after Botox maker Allergan announced its own interest in making an offer.