Overton was struck in the ribs while batting in the second test at Adelaide and aggravated the area further while fielding in the third test in Perth with scans revealing a fracture.
Australia have already reclaimed the Ashes with their innings and 41-run victory in Perth giving them an unassailable 3-0 lead in the five-match series.
Curran, who made his Twenty20 debut in June and then played his first one-day international in September, was an injury replacement for Steven Finn, who withdrew before the first test with a knee injury.
Root said the selection of the South-African born fast-medium bowler was very much a gut decision.
“Sometimes as a captain you have to go with your gut and he really hit home with me this week,” Root told reporters ahead of the fixture starting on Boxing Day at the Melbourne Cricket Ground.
”It wasn’t an easy decision. We certainly (spent) a while thinking about it, trying to weigh up what was going to be the best way to go about it in these conditions and on this surface.
“He does get the ball to move around a little bit. He’s always in the contest. That’s one thing that really stands out to me - he will at no point hide away from any challenge if it does become very hard. He’ll give it absolutely everything.”
Curran’s elevation ahead of Wood was something of a surprise given England’s pace bowlers have struggled in Australia, with stalwarts James Anderson and Stuart Broad both struggling to get any movement through the air or off the pitch, while their entire attack has been lacking in pace.
Pundits had suggested that Wood, arguably the fastest bowler in their squad, could be picked, but Root said the 27-year-old was not quite match-fit as he battled back from an ankle injury.
“He did come into it,” Root said of the selection discussions around Curran and Wood.
”The fact that (he‘s) not necessarily 100 per cent fit, not played a huge amount of cricket, (it) might have been a little bit of a risk going into this game.
“It was a tough call (but) ...for the balance of the team, I think Tom was the best option.” REUTERS