Defense Primer: Command and Control of Nuclear Forces [Updated December 11, 2018] [open pdf - 415KB]
From the Document: "The U.S. President has sole authority to authorize the use of U.S. nuclear weapons. This authority is inherent in his constitutional role as Commander in Chief. The President can seek counsel from his military advisors; those advisors are then required to transmit and implement the orders authorizing nuclear use. But, as General John Hyten, the Commander of U.S. Strategic Command (STRATCOM), noted during his September 2016 confirmation hearing, his job is to give advice, while the authority to order a launch lies with the president."
CRS In Focus, IF10521
Congressional Research Service: https://crsreports.congress.gov/