WASHINGTON—The Senate voted overwhelmingly Monday to confirm James Comey, a former Bush administration official, as the next director of the Federal Bureau of Investigation, after Sen. Rand Paul removed a procedural hurdle to the nomination.

The vote was 93-1. Sen. Paul (R., Ky.), the sole lawmaker voting against the confirmation, had held up a vote on Mr. Comey since June over concerns about the FBI's use of surveillance drones on U.S. soil. He said such drones had been deployed before a sufficient policy on their use was...