Hughes and Ireland previously worked together at Manchester City during the latter's time at the club from June 2008 to December 2009.
Speaking to the official Stoke website, Ireland said: "I had a great relationship with Mark at Manchester City and I was desperate to work with him and his staff again.
"Mark knows how I play and how to get the best out of me."
Following an £8million move from City three years ago, Ireland has made just 57 Villa appearances in all competitions.
Although 17 of those were under Lambert last season, Ireland has not figured since January and is now naturally desperate to play again.
"I just want to get a good run of games, which is something I haven't had for a while," added Ireland.
"I do feel as though I've something to prove and I'm coming here to get myself back playing.
"There are still lots of things I want to achieve. I've set myself a lot of goals and want to hit the ground running. I turned 27 last week and to me it's vital I'm playing on a regular basis.
"I'm so grateful to Stoke for the opportunity. I'm looking forward to getting stuck into training and building my career back up again."
Like Ireland, Arnautovic has on occasion found himself in the spotlight for the wrong reasons.
Mourinho added at the time that: "Mario Balotelli is his best friend and coincidentally they have the same properties. This is not easy."
Arnautovic once had a fall-out with former Werder Bremen general manager Klaus Allofs and a training ground bust-up with a team-mate, Sokratis Papastathopoulos.
Stoke chairman Peter Coates appreciates in Ireland and Arnautovic, Hughes has seemingly signed two difficult characters, but has no doubts he will get the best out of them.
"Mark has been out to see (Arnautovic) in Germany and likes him," said Coates to The Sentinel.
"He's got a bit of a chequered history on the personal side, but he is coming to a club with a squad of good professionals and that should be good for him.
"Certain clubs work for certain players and we are hoping he's going to be the striker who can score the goals for us because that has been one of our deficiencies.
"Friends of mine at Manchester City remember Ireland coming through the system there and he has since had his moments.
"His career seems to have gone in the wrong direction of late, but Mark knows the guy well and he certainly has a good pedigree as a player."
- Sports & Recreation
- Manchester City
- Marko Arnautovic