Gale believes Root is the right man to lead England forward after Cook stepped down following four years in charge.
Root is widely expected to be named Cook’s successor before England leave for their one-day series in the West Indies a fortnight tomorrow.
Yorkshire first-team coach Gale said the 26-year-old is the standout candidate and has all the right qualities to succeed.
“I think Joe would do a terrific job,” said Gale.
“He’s got a brilliant cricket brain, he speaks very well, and he’s highly respected by his team-mates too.
“At this moment in time, I don’t really see any other candidate.
“It’s probably not completely cut-and-dried, but, for me, there’s only really Joe Root.”
Root has limited captaincy experience having led Yorkshire three times in first-class cricket and England Lions once.
The Yorkshire dressing room cheekily dubbed him “craptain” after Middlesex chased 472 to beat Yorkshire at Lord’s in 2014.
It was match for which then club captain Gale unselfishly dropped himself to make way for the returning England batsman.
However, few players have the luxury of captaining their counties for any length of time before assuming international office, and Gale believes Root’s captaincy inexperience counts for little.
“Joe’s had a little bit of experience doing it for Yorkshire, albeit not a great deal, but this sort of thing is usually the case with the England captaincy nowadays,” he said.
“You don’t always get the chance to do much captaincy at county level, and I’m confident he’d do a really good job.
“People always talk about that Middlesex game many moons ago, but I’m sure that if I’d been leading the side, the result might have happened anyway.
“Joe’s shown over the years that when the pressure’s on, he thrives on it, and I don’t think that the step up to the England captaincy would affect his batting either.”
Gale’s comments were echoed by Yorkshire’s director of cricket Martyn Moxon, who described Root as “a natural leader” whose time has come.
“When is the right time? That’s the $64,000 question, but I don’t think it (the captaincy) would be a problem for Joe,” said Moxon.
“It is something he would have to adapt to, but I think he is the type of cricketer who would thrive on it rather than it being a problem for him.
“The responsibility would suit his character.”
Root, the current England vice-captain, would likely favour a more attacking style of leadership than Cook, who was often criticised for a conservative approach.
Gale believes criticism of Cook has been over-the-top and he praised his contribution to English cricket.
“I think he has been an outstanding captain,” said Gale.
“I think his contribution has been excellent, and he’s a good man – a genuine good guy of the game.
“He’s had some unfair criticism at times, but his record speaks for itself, both as a captain and with the bat.
“Everyone’s got their own style and his style worked; he won two Ashes series and he’s created a group of players like the Joe Roots, the Jonny Bairstows, the Ben Stokes, a new era.”
Cook stepped down after 59 Tests in charge in the wake of the 4-0 defeat in India.
He cut a dejected figure after that series and has now chosen to focus on his batting.
“Stepping down has been an incredibly hard decision, but I know this is the correct decision for me and at the right time for the team,” said Cook.
“I’ve had time to reflect after the India series and this weekend I spoke to Colin Graves (England and Wales Cricket Board chairman) to explain and offer my resignation.
“It’s a sad day personally in many ways, but I want to thank everyone I’ve captained, all the coaches and support staff and, of course, the England supporters and the Barmy Army who follow us home and away and have given us unwavering support.
“Playing for England really is a privilege, and I hope to carry on as a Test player, making a full contribution and helping the next England captain and the team however I can.”
Andrew Strauss, director of England cricket, paid tribute to Cook and insisted that he did not try to talk him out of his decision.
“His country owes him a great debt of gratitude,” said Strauss.
“He’s led the team with determination, conviction and a huge amount of pride.
“This wasn’t one of those situations when it was right for me to persuade him to carry on.
“I’ve been there myself; you either know if you have got it in you to carry on, or, deep down, if it’s time to step aside.”
Relinquishing captaincy can aid Alastair Cook: Page 19.