The White House said the President was acting on the recommendation of the Committee on Foreign Investment in the United States, which reviews foreign purchases of US companies, to reject the proposed $117bn offer on national security grounds.
It would have been the most valuable tech takeover in the world had it gone ahead.
Broadcom had gone directly to shareholders after a previous offer was rejected by Qualcomm.
Its bid interest was blocked at a sensitive time – given the world is gearing up for the roll-out of ultra fast 5G mobile services and Mr Trump’s wider agenda to protect the interests of US companies.
The committee had warned that “a shift to Chinese dominance in 5G would have substantial negative national security consequences for the United States.
“While the United States remains dominant in the standards-setting space currently, China would likely compete robustly to fill any void left by Qualcomm as a result of this hostile takeover.”
Broadcom, which had pledged to move all its headquarter functions to the US if it won the day, said it “strongly disagreed” with the reasoning behind the decision.
The committee had raised concerns that any takeover may hinder progress in achieving 5G mobile networks because of Qualcomm’s current position as one of the leading makers of processors that power smartphones.
It also holds key patents which earn massive royalty payments from phone makers, such as Apple.
Broadcom chief executive Hock Tan had written to US policymakers last week to argue that legal claims Qualcomm is facing, alleging abuse of its patents to damage competition, should be seen as a risk to Qualcomm’s 5G investment.
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He had pledged a $1.5bn investment in 5G in the US if Broadcom secured the takeover.
Mr Trump’s decision was also widely seen as an extension of his protectionist agenda that has seen him pledge to impose tariffs on imports of steel and metal products from later this month.