The 57-year-old was out of contract at Huish Park following their League One play-off final success over Brentford last month but having returned from holiday he put pen to paper on a new contract on Wednesday along with assistants Terry Skiverton and Darren Way.
Johnson said: "It is exciting for me because it is taking our club to the next level. Who wouldn't want to be a part of what we've achieved over the last few years and certainly over the last few weeks?
"It is great for me now to settle down and talk to the players because I am now going to be the manager here for the next couple of years at least.
"Little old Yeovil deserve the little old manager and here I am. I tick all those boxes."
Johnson, who spoke of the need to add quality to his squad ahead of their maiden voyage into the second tier, admitted the hard work going in off the field meant he never considered leaving Somerset.
"The chairman has been talking to me and I've been talking to him and I'm seeing that the club still wants to progress and is still working very hard to make sure we can compete at the Championship level," he said.
"I've seen the tractors and all the stuff on the training ground which means a lot to me and the pitch out there. Lots of little things have to happen and we've got those assurances.
"It was just a matter of agreeing terms and that was comfortable as well. None of us are greedy, I know what the club have got and what they've got to give. They gave it and kept me and my staff happy.
"We certainly had no other thoughts other than taking Yeovil into the Championship campaign this season."
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- Terry Skiverton