Buttler missed their 157-run defeat at The Oval to attend the birth of his second child but has been recalled as England head into the final Test trailing 2-1.
Bairstow replaced Buttler behind the stumps and took five catches in the match but fell for a duck in the second innings when England's chase unravelled on the final day.
"Jos will be back as the vice-captain and the wicketkeeper," Root told a virtual news conference on Wednesday.
"He's the vice captain of this team. He is integral to what we're about.
"I know his output in terms of runs this series hasn't been as high as he would have liked, or as we would like, but we know what a great player he is."
Asked if it was harsh to ask Bairstow to vacate the wicketkeeper's role after one match, Root said: "I think Jonny knew exactly what the scenario was when given the opportunity to keep wicket last week."
England have also recalled left-arm spinner Jack Leach but Root made it clear that all-rounder Moeen Ali remained their number one spinner.
"I'm sure Jack will be desperate to take an opportunity if granted one, but we've not seen the pitches," Root said.
"We know what you can get sometimes here at Old Trafford, it can spin and that could be an option that we have to look at with two spinners."