Begovic represented the Blues for two years between 2015 and 2017.
He told talkSPORT: “It's a seven-year deal and he's at a great age so I think this is someone Chelsea can really build around for many years to come.
“I think he was performing quite well at Bilbao, coming through the ranks there and trying to break into the national team.
“So he's definitely been on the scene for a little while.
“From Chelsea's view, this is a long-term move."
Asked whether the world-record £71.6m transfer fee represented good value, Begovic was nonplussed by the amount his former side spent.
“That's just the way the market is going," added Begovic who is now Bournemouth's No.1.
“Some prices are being thrown around and this is the price of doing business these days."