Coleman has just committed to a new deal as Wales coach.
Williams said: "I'm happy at the news. It's quite obvious around the squad that we enjoy working with him and being in camps and from my point of view always I've said that and always knew probably be the case so we're happy.
"There was a lot going on, reading what was being written in the media, but I never doubted he wouldn't stay because after a tough start you can see he's enjoying it and we enjoy working with him.
"He's a good guy, we have a good rapport with him and I like the way he's so hands-on in training and with his meetings. All round he's good to work with so hopefully now we can start to pick up results."
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