"It feels amazing," he told Sky Sports on Wednesday. "I think as a young kid when you're growing up you always aspire to be England captain. It's sort of the pinnacle of the test arena isn't it?"
Asked about how his relationship with Cook - who resigned last week - would work, Root told the BBC that he was not afraid to ask for help.
"It would be silly not to take advice from Alastair and the other senior players, but I will want to do things my way as well," he added. "You shouldn't be scared of asking for help, but I would also like to think I can put my stamp on it."
The 26-year-old said Cook had been in touch to congratulate him on his appointment and that the former skipper would continue to play a key role in the dressing room.
"We've exchanged a few text messages," Root said. "He's tried to let me have a bit of space for now but I think we'll definitely be in contact over the next few days.
"One thing that Cookie will naturally do is let me go about things my way. He's a very respectful bloke."
Root also dismissed concerns that a lack of leadership experience might hamper him in his new role. He has previously captained Yorkshire for four first-class matches, but has served as England's vice-captain for the past 18 months.
"I think I've played 50-odd test matches now," he added. "The experience in that arena counts for a lot. I think it's very different cricket, test cricket to county championship cricket.
"Over the last couple of years I've had the added responsibility of the vice-captaincy.
"For a while now, I'd like to think that even though I haven't been captain I've been trying to think like a captain as much as possible to try and help Cookie out."
(Reporting by Simon Jennings in Bengaluru. editing by Pritha Sarkar)
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