Hughes swapped Kenwyne Jones for Odemwingie during the January transfer window.
It wasn't the first time the Welsh manager had made a move for the Nigerian but he was pleased that it eventually went through.
Hughes said: "I tried to get him in the summer but unfortunately he went to Cardiff.
"But when you miss out on players you keep an eye on them and wonder if something might come off in the future.
"I didn't anticipate the opportunity would come up quite so quickly but we got him and he's had an immediate impact.
"It's well known we had issues with Kenwyne and needed to look at options. When the possibility of getting Peter came up we were more than happy."
Stoke face Hull City on Saturday afternoon in the Premier League.