Johnson fought off competition from Chesterfield's Paul Cook and Bournemouth boss Eddie Howe to pick up the award at the ceremony at The Brewery, London on Sunday evening.
The former Bristol City boss led the Glovers into the Championship for the first time in their history with a Wembley win over Brentford in May.
"It feels great to win this award, it's a fantastic achievement for our football club," he told the Western Gazette. "There are so many unsung heroes at Yeovil Town that also deserve this.
"They were trying to get in the league for 108 years and we got it 10 years ago and now we've had a fantastic decade in the Football League.
"When we got our promotion from the Conference to the Football League you wouldn't think we would get to the Championship by now, and to do it via Wembley was fantastic.
"There are only 40,000 people in Yeovil and we took 25,000 to the match. I'm accepting this award on behalf of everyone associated with the club."