Root asked to be added to the squad at his home Headingley ground, targeting one more innings to find the form that eluded him in the recent matches against New Zealand.
He scored 39 runs in four innings against the Black Caps, who will also take on England in the opening game of the World Cup in Ahmedabad.
Root's presence is welcome for Zak Crawley (25), standing in as white-ball captain for the Ireland series in place of the resting Jos Buttler (33).
"I love spending time with Rooty. To have him in the side as a batsman and former captain is going to be tremendously useful for me and the team," he said.
"It's great having him here. Especially so for me as captain, because I can lean on him for that kind of stuff. I played under him for a long time and stood next to him at slip when he was Test captain.
"It's great to have him in the team and I will look to him. He's a great cricket brain and experienced guy.
"No one works harder than Joe, that's why he's the best. We all try to emulate him as much as we can. He's a great person to learn from and a role model for us all. I hope he gets what he needs from it too."