The 35-year-old Root will return as Test skipper later this month, four years after resigning from the role, when England host Pakistan for a three-match series.
The ECB confirmed Fleming and Root's new roles on Thursday, succeeding Brendon McCullum and Ben Stokes, who retired following a four-year spell as captain, respectively.
Fleming had input about who he wanted as his captain, according to England's managing director Rob Key, and Root cannot wait work with the former New Zealand skipper.
"If I'm being brutally honest, it (Fleming's appointment) was a big reason why I wanted to do it," Root said in a video posted by the ECB. "I'm very excited by the way he sees the game, where he sees us sit as a team, and the work that we have to do to get to where we want to get to. All of that got me very excited about taking this role on.
"I'm very much looking forward to working with him. He's obviously got a wealth of experience and done some amazing things within the game as a player and as a coach, and I'm very much looking forward to the next little while, and us trying to build something pretty special together."
Root had a mixed record as England Test captain in his previous stint, which lasted five years, with 27 wins, 27 defeats and 11 draws.
He worked alongside two permanent head coaches, Trevor Bayliss and Chris Silverwood, between 2017 and 2022, and said he would take inspiration from the way Stokes and McCullum had led the team.
Root added: "The last four years have been the most fun I've had in professional cricket, and a big part of that was down to the way that they got me to see the game, how I fit into that side, and the experiences that we managed to create on and off the field.
"Clearly, the last little while is probably what's fresh in everyone's mind, but you're looking at a four-year period where we did a lot of amazing things.
"I've taken a lot from that, and I feel it will be a big part of how I want to approach things moving forward as a leader of this team.
"The thing that stands out the most for me is the shift in mindset that was created around how we want to play the game: trying to strip the fear away from things, make sure guys feel that they can really just allow their talent to come out as frequently as possible, and in big moments in games. The more that can happen, the better."
Root will work with interim head coach Marcus Trescothick for the series against Pakistan, with the first Test set to start on 19 August at Headingley.
England continued their dominance over Sri Lanka with a comfortable 89-run victory in the first ODI at Chester-le-Street as spinner Will Jacks picked up his maiden five-wicket haul.
England fast bowler Mark Wood has made the decision to retire from international cricket with immediate effect after being plagued by injuries.
Stephen Fleming says he would "love to be in charge of the number one Test team in the world" as he steps in to become England's head coach in the longest format of the game.
England completed a clean sweep of victories in the three-match T20I series against Sri Lanka after a convincing eight-wicket win in the final clash at Old Trafford on Sunday.
