Johnson guided the Nationals to their first winning record since moving to D.C., in 2005, posting a Major League-high 98 wins in the regular season.
"To be recognized by my fellow comrades, a particularly accomplished bunch, makes this award especially meaningful," Johnson said in a statement. "To put on the uniform every day and compete is an honor I never take for granted."
The award was voted upon by NL managers. Johnson received four votes, while Reds manager Dusty Baker received three.
San Francisco's Bruce Bochy and Milwaukee's Ron Roenicke also each received one vote.