The former Wales, Blackburn, Manchester City, Fulham and QPR boss has taken over at the Britannia Stadium after fellow Welshman Tony Pulis left the club.
He was formally unveiled at the Britannia Stadium on Thursday.
Former Manchester United striker Hughes, 49, had been out of work since November, when he was sacked by QPR after a tough 11 months in charge.
Asked if he needs to rebuild his reputation, Hughes said: "Yes, possibly.
"I've 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 games at the beginning of last season.
"I understand that, but maybe it gives me more motivation to prove people wrong.
"I have kept my counsel for six months, and haven't really come out and said my piece of the story. Now is not the time to do that, but I've listened to what people have said about my ability as a manager and I can assure everybody I will use that as a motivation to do well for Stoke."
Pulis left the Potters by mutual consent after seven years in charge last week. He achieved promotion with the club and established them as a Premier League club, but spent a great deal for little improvement in style recently - leading to disgruntlement among the fans - and they flirted with relegation this season before finishing 13th.
Hughes led Blackburn to three successive top-10 Premier League finishes and two FA Cup semi-finals before leaving for Man City in 2008. Replacing Sven-Goran Eriksson, he did not bring much success until he was sacked the following year and replaced by Roberto Mancini.
Six months later Hughes took over at Fulham. He left after just a year in charge, stating that he wished to further his experiences as a young manager, but was again out of work for six months before joining QPR.
Pulis guided the Potters into the top flight in 2008 and they have stayed there since, also reaching the FA Cup final in 2011 and subsequently playing in the Europa League.