The 31-year-old midfielder was announced as Stoke's second signing of the close-season on Monday, having been released by Fulham following their relegation from the Premier League.
Hughes was the man who signed Sidwell for Fulham from Aston Villa in January 2011 and Sidwell is looking forward to linking up with the Welsh manager once again at the Britannia Stadium.
He told Stoke's official website: "There were two factors behind my decision to join Stoke – the first being the fact that it's a club that is really moving forward.
"I was really impressed with the football Stoke played last season; the way they played against Fulham on the penultimate weekend of the season really had a wow factor about it and it led to a first ever top-10 finish in the Premier League.
"Then there's the manager because he's a man that I have the highest regard for. He signed me for Fulham and I really enjoyed the time I worked with him there.
"I like the way he asks his teams to play and his training sessions are good, which makes coming into work on a daily basis really enjoyable."
Fulham's relegation was confirmed following a 4-1 defeat at Stoke which saw Felix Magath's men comprehensively beaten.
"Relegation was difficult to swallow, especially the way we went down," said Sidwell.
"We were, of course, relegated at the Britannia Stadium on a day when we didn't really give it a go. We rolled over.
"I had three-and-a-half years at Fulham and it's disappointing that my time with them ended on such a sour note with relegation, but joining Stoke is a new chapter and I'm really looking forward to the future."
It is thought Hughes will look to add to the capture of Sidwell by landing a third player out of contract in the coming weeks, with former Manchester United striker Mame Biram Diouf also on Stoke's radar.