At the regular election held in any State next preceding the expiration of the term for which any Senator was elected to represent such State in Congress, at which election a Representative to Congress is regularly by law to be chosen, a United States Senator from said State shall be elected by the people thereof for the term commencing on the 3d day of January next thereafter.
2 U.S. Code § 1 - Time for election of Senators
The first section of Amendment XX to the Constitution provides in part: “* * * the terms of Senators and Representatives [shall end] at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin.”
Time for election of Senators, see Const. Art. I, § 4, cl. 1.
Vacancies in the Senate, see Const. Amend. XVII.