The team announced the move Wednesday, along with placing pitcher Joe Ross on the 60-day disabled list as he recovers from Tommy John surgery in July.
The Nationals didn't release terms of the agreement, though a person with knowledge of the deal told The Associated Press on Monday that it was for $1 million. The person spoke to the AP on condition of anonymity because the deal wasn't official at the time.
Benoit is a right-hander who first reached the big leagues in 2001. He has played for eight teams, finishing last year with Pittsburgh.
He has 764 career appearances, going 58-49 with a 3.83 ERA and 53 saves.