The national team boss is looking for a fresh start after his side kicked off their World Cup 2014 qualifying campaign with two defeats.
Ramsey was named captain just over a year ago by former manager Gary Speed, making him the youngest-ever skipper of the national side aged just 20 years and 90 days.
"I think he has felt the pressure of it," Coleman told reporters.
"We need to go in another direction because what we have been doing has not been working so I wanted to make some changes - and that was the biggest one really.
"It was not an easy decision. Of course he was disappointed. I spoke to him yesterday and he was incredibly mature about it - and a little bit relieved, if I'm honest, because it is a big pressure.
"I was very impressed with what he had to say and his reaction, he was very professional."Ramsey's replacement Williams is not short of experience with 36 caps, and is already the captain of his club side.
And Coleman is confident in the 28-year-old's ability to step up to the pressures of leading the national side.
"As a captain of your country, everyone wants to do it but not everyone can," added Coleman.
"I've no doubt Aaron will be the captain again one day. When I took the job I was very mindful that whatever Gary had done was working and as much as I possibly could I kept it the same.
"But now it is not working - and I want to go in another direction, which I will do.
"Ashley will be the skipper. He is a natural leader. He is a very good player who has great experience."