For years, Hock Tan studiously avoided the limelight, even as he built a onetime division of Hewlett-Packard into what is now Broadcom, a semiconductor maker whose chips help power the newest iPhone.

Yet there he was last Thursday, standing beside President Trump at the White House and announcing plans to move his company’s legal headquarters from Singapore to the United States. Mr. Trump heralded the move as an endorsement of his business-friendly tax plan and called Broadcom “one of the really, great, great companies.”

On Monday, another reason for the move became apparent. Mr. Tan announced that his company had offered to buy another major chip maker, Qualcomm, for $105 billion, in what would be the biggest takeover in the history of the technology industry. The combined company’s products would touch nearly every smartphone in the world.

It is a deal that may be more likely to receive regulatory approval with Broadcom based in the United States — and with the president on Mr. Tan’s side.