Fallon, 65, stepped down as UK defence secretary saying his conduct may have fallen below the high standards expected amid revelations that he had made unwanted advances towards a journalist years ago.
Prime Minister Theresa May promoted Williamson, her trusted chief whip, to the job of defence secretary to fill the role.
The 41-year-old Williamson, the MP for South Staffordshire, has been responsible for exerting discipline over the prime ministers fractious parliamentary party since last year.
Williamson was closely involved in negotiating the confidence and supply deal with the Democratic Unionist party that secured the parliamentary support May needed to govern in the aftermath of June's general election.