The League One side defeated Accrington Stanley 2-0 in a Second Round Replay, earning a glamorous home tie with the Premier League giants on Sunday 4 January, live on BT Sport.
After seeing Simon Gillett and Kieffer Moore fire his side to victory, Glovers boss Johnson said: "I know Accrington are a league lower and everyone will say we didn't do it convincingly enough, but that won't matter when Man United run out on the Huish Park pitch."
Yeovil Town v Man Utd
The FA Cup
Third Round Proper
3.30pm, Sunday 4 January 2015
Winning club will receive £67,500 from prize fund
United have met Yeovil once before in the competition back in 1949, with the Red Devils winning 8-0 at Maine Road, and Johnson is delighted to have secured a home tie against the 11-time winners.
"I'm always so proud of the club when we come through a game like this," he told BBC Somerset.
"I knew what this meant to the club, me, my family, our directors, supporters and my management team.
"There was no prize greater than this one. And now we've got the game against probably the world's biggest team. That's the one to look forward to now."
And with his side currently sitting bottom of League One after suffering relegation from the Championship last season with one of the smallest budgets, Johnson explained how important the money his side earn from their Cup run will be.
They will receive £27,000 for their Second Round win win and £144,000 from their televised game with United – and Johnson says it is vital.
"I didn't want to use the word 'massive' for finances, but it is for a club like us. You can't sell a player for a quarter of a million, or half a million, so you have to get it in other ways.
"If the FA Cup draw is good to you, then it's the only other way of getting it. We've got it and I'm sure the directors will be smiling. They've got what they were praying for."