Mangione admitted to charges stemming from the fatal shooting of Thompson, a case that drew national attention and prompted intense public debate.
The federal stalking counts allege that Mangione targeted Thompson before the December 2024 attack in Manhattan.
Prosecutors have also accused Mangione of traveling across state lines and using a firearm in connection with the killing.
The plea resolves the federal stalking case but does not necessarily end the broader criminal proceedings. Mangione still faces separate state charges, including murder, in New York.
Thompson was shot outside a hotel as he arrived for an investor conference. Authorities arrested Mangione days later in Pennsylvania, where he was found carrying documents that investigators said connected him to the case.
The federal case could still carry severe penalties, depending on the final sentencing terms and how it interacts with the pending state prosecution.