Hughes has moved to recruit the Cardiff City forward to add to his attacking options, with Kenwyne Jones going in the opposite direction.
An agreement was reached on Saturday for the player exchange and Hughes has no worries about Odemwingie's transfer being tied up quickly.
He believes Odemwingie has all the attributes needed to be successful at Stoke.
Following Sunday's 1-0 FA Cup fourth-round loss at Chelsea, Hughes said: "It should go through tomorrow and will be concluded then.
"We're pleased to get Peter in. He's a good Premiership player with experience at this level, a goal in him and a bit of pace - which we need to add to the squad.
"(I'm) Pleased to add him."