President-elect Donald Trump appeared to have announced that Johnson would become the next ambassador earlier Thursday.
Trump was speaking at a luncheon in Washington when he introduced a guest as "sitting next to the ambassador Woody Johnson, going to Saint James."
Trump said, "Congratulations, Woody."
The appointment has not been formally announced, but Johnson was considered a favorite for the job. The billionaire businessman and philanthropist from the Johnson & Johnson family has known Trump for years.
Johnson originally backed Trump rival Jeb Bush in the GOP primary.
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The Associated Press contributed to this report.