In what was seen as an unusual move Trump said that "there is credible evidence," that the proposed bid could lead to "action that threatens to impair the national security of the United States."
The move by the President follows a review by the Committee on Foreign Investment in the United States (Cfius) which had concluded that it was minded to refer the deal to the administration for rejection.
While Broadcom strongly disagreed with the committee's findings which suggested there were "potential national security concerns" there were also concerns, again highlighted by the committee, that investment in research at Qualcomm would be cut back should the takeover go through.
While Broadcom promised to maintain levels of research and development and not to sell off any "critical national security assets" it appears that was not enough for the US authorities.
It comes at a time of growing protectionism in the US and it was thought that allowing the purchase of a leading semiconductor company by a foreign company would weaken the position of the US, to the benefit of China.
The administration is said to have been concerned about the US losing its leading position in 5G technology which is seen as being critical to the next generation of wireless devices and technologies.