The former Manchester United striker replaces fellow Welshman Tony Pulis who left the Premier League club by mutual consent last week after seven years in charge.
"I'm really grateful... they've looked maybe beyond my last position and taken my career as a manager as a whole," Hughes told a news conference at the club's Clayton Wood training ground.
"Mistakes were made [at QPR] and certainly I made mistakes which I will learn from," added the 49-year-old.
"I have had something like 270 games at Premier League level and people in recent months possibly have wanted to define my managerial career on the basis of 12 months of last season... maybe it gives me more motivation to prove people wrong."
Hughes was sacked by QPR in November, departing after a miserable start to the season with the West Londoners, at that point the only club in England's four professional divisions not to have recorded a win.
In total, he won only eight of his 34 games in charge at Loftus Road.
The former Blackburn Rovers, Manchester City, Fulham and Wales manager was replaced at QPR by Harry Redknapp who failed to stave off relegation.
SUSTAINABLE MODEL
Hughes said he had kept quiet for the past six months but had listened to what people had said and would use that positively at Stoke.
"My intention is to take this club and team itself forward and make sure we are successful in the future," he said.
"The success Tony had enables me to have a better chance because I'm following somebody who has put in place things that enable the club to be stable and has created an environment that is conducive to being successful in the Premier League."
Stoke chairman Peter Coates would not be drawn on how much spending money Hughes would have and said the club wanted to be "sustainable".
"It's a great blot on the Premier League that there is so much debt when there's so much money," added Coates. "We want to have a sustainable model, we can do that and still provide funds for the manager."
Coates said Hughes was the right fit for Stoke, with a record that spoke for itself.
"We also understand that whoever we choose, some people will disagree and I don't have a problem with that," he said.
"Those who focus on QPR, that's fair enough, but they should look at the bigger picture and see what he has achieved throughout his career.".
Stoke, who finished 13th in the 20-team league last season, parted company with Pulis after the abrasive style of football he oversaw led to some disgruntlement from fans.
Hughes said the club had a strong squad and he would not come in and "wipe away all the hard work that's been put in place in previous seasons.
"What I will look to do is hopefully make them a little bit more offensive and I'd like to think the teams I've been involved in have always scored a good level of goals," he added.
"But we're not going to chuck the baby out with
