The Potters confirmed the signing of the Swiss midfielder from Inter Milan for a club record fee of £12million on Tuesday when the 23-year-old agreed a five-year contract with the club.
Coates told the club's official website that this type of signing proves the Potters are beginning to be a major player in the transfer market.
"I'm not sure how long it has gone on for – quite a while I would suggest, but football is a messy business and signings like this can take a while to conclude," he told the club's official website.
"We are obviously very pleased that he is here though, because he's an excellent player and one that we feel will do very well for us.
"He has been an important target and we are very pleased and I know more importantly Mark and his team are delighted to have him on board.
"I keep saying we are trying to get better and this is another good example of the progress we are trying to make."