The Bath flanker damaged knee ligaments in England's first warm-up international against Wales on August 6 and initially feared he would miss the tournament altogether.
Moody was "annoyed" at England's medical staff when they stopped him from playing in last weekend's opening game against Argentina - but he has finally been given clearance to play.
"It's been a frustrating few weeks for me with injury but I feel fit now and it is a great chance to get out on the pitch," said Moody.
"Captaining England for the first time at a World Cup will be very special - but just being on the pitch is the most special.
"Maybe for the first couple of seconds when I got injured at Twickenham I thought that was it but I have had the support of a fantastic medical team and it has come good.
"The World Cup is the pinnacle of your playing career and it is what every player strives to be involved in,
"Taking part in the warm-up against Argentina was probably the most annoying period of my life - taking part for 20 minutes, getting hot and then having to sit in the stands.
"I love playing for England, I love being involved in this squad and it is a massive privilege to be captain of it, but just to be playing the sport I love with a group if players I respect is the most important thing."
Moody's leadership will have been tested this week following critical reports of the night out in Queenstown enjoyed by some of the players last Sunday.
The squad held a team meeting on Thursday and, according to those who were there, emerged from it tighter and more determined than ever to succeed in New Zealand.
Johnson outlined Moody's value to the squad and hailed his return to action, along with scrum-half Ben Youngs who also travelled to New Zealand under an injury cloud.
"We came with a couple of guys who had injuries and hadn't played that much," said Johnson.
"It was good to get Ben on the field last week and now to get Lewis out there this week.
"He's captain for a reason and he brings a lot to the team in terms of leadership and setting a great example."
Georgia lost 15-6 to Scotland on Wednesday and Johnson agreed it was unfair on them to have to play England just four days later.
But he said: "I don't disagree with a lot of it but we are here to play a game. They will have no sympathy for us and we will have none for them when we kick off."
Johnson and Moody both played in England's only other meeting with Georgia, an 84-6 victory in the opening game of the 2003 World Cup in Perth.
Georgia have taken great strides since then - pushing Ireland close at the last World Cup - and Johnson insisted England would not under-estimate the threat of a side that includes some of the best players in the French Top 14.
"Eight years ago when we played them it was all very new. A lot more of them are playing at the very highest level now in Europe," said Johnson.
"These guys are fit and professional players. We are at the point now, if you ever doubted it, where if you get it wrong they will make it difficult for you.
"We talk about their directness and physicality and they have more than they showed against Scotland.
"They are very good and you will only see that increase over the years. They lost 14-10 to Ireland at the last World Cup and we are under no illusions about what we have to do.
"If you lose the physical battle in rugby you will probably lose the game."
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