"They're the best at what they do in my opinion," Hughes told the club's official website.
"That is why they have worked alongside me for so long. They are both outstanding coaches, while they also have a real understanding of the game and how I like things to be.
"So that means when you go to a new club, you hit the ground running and everybody in the squad is up to speed.
"I'm pleased that they are joining us because I'm sure I will benefit from that and so too will Stoke City."
Chief executive Tony Scholes said: "Mark Bowen and Eddie Niedzwiecki have been key members of Mark Hughes' backroom team for some time now and he was therefore eager to have them working with him once again here.
"They both have outstanding pedigree as coaches and we are delighted that they have now agreed to join Mark's new team."