Villa will pay Albion an initial £6m for the former Hull City defender who has signed a four-year-deal at Villa Park.
Albion paid £6m up front to Hull City last summer for Chester in a deal totalling £8m, but because he only made 12 Premier League appearances he failed to trigger the majority of the extra fees.
"James has been sold to Aston Villa," confirmed Pulis. "He's a great lad, he had a fantastic Euros, I was out there and he had a great tournament.
"He's not played regular football and he wanted to play, he was desperate to play regular football.
"The club's made a profit of nearly £2million in a year, it's a good deal for James, it's a good deal for the club.
"As long as we can reinvest and get those players that we want in."
Chester is Albion's most expensive defender of all time, but he endured a frustrating time at The Hawthorns.
Pulis insisted on playing the Warrington-born defender in an unfamiliar position of full-back, when Chester openly admitted he'd rather play centre-back.
He featured in that favoured role just one time last season.
When asked why Chester was being sold, Pulis said: "It just didn't work out and sometimes it doesn't work out.
"We've had a great deal. Chessy's had a great deal, we've shaken hands, it's a clean cut and we move on."