The Collierville Republican resigned his legislative seat in a Nov. 1 letter to Gov. Bill Haslam. Senate spokesman Adam Kleinheider says Norris was sworn in Thursday in Memphis by Judge Jon Phipps McCalla for the U.S. District Court for the Western District of Tennessee.
President Donald Trump nominated Norris to the federal bench in July 2017. He was confirmed on Oct. 11.
In his resignation letter, Norris said it was an honor to represent Senate District 32 since 2000. He called serving as majority leader since 2007 the "opportunity of a lifetime."
A special election will be scheduled to fill the remaining two years of Norris' Senate term.
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