The Glovers' rise to the second tier of English football for the first time in their history and comes just ten years after they were promoted to the Football League.
First-half goals from Paddy Madden and Dan Burn were enough to give Yeovil a 2-1 win over Brentford in the League One play-off final, as the Bees could only get one back through Harlee Dean.
"It is a great achievement for our club," Johnson told Sky Sports.
"This is for everyone who has been a part of it for ten years and everyone who has been a part of it over the last year.
"I know what it is like to lose here so commiserations to Brentford, they give it a right go like they would do at Wembley but we held out and our supporters were fantastic and they saw us through the second half."
Johnson admits it is one of the highlights of his managerial career.
"It is one of them and at this moment of course it is one of the best," he said.
"But to have these 20,000 fans supporting us for a relatively small club, on a small budget, this is what you can do. If you have got big ambition for a little man, you can get there."