On Thursday, the Toffees confirmed that Silva had been appointed as the replacement for Sam Allardyce, with the Portuguese penning a three-year deal at Goodison Park.
Jagielka has revealed that a number of friends have played under Silva at Hull City and Watford, and each of them have spoken highly of the new arrival.
The 35-year-old told the club's official website: "Everyone I've spoken to about him has said they've really enjoyed playing under him.
"I've got a few good friends at Watford and Hull and I haven't heard a bad word said about him. He's got high standards. He'll expect us to work hard and train hard - and he'll let us know exactly what he expects from us.
"I know the players and the fans will all get behind him. We have a new manager and new ideas and everyone will be super excited."
Jagielka is expected to feature in Silva's squad, with the long-serving Englishman still having one year left on his contract.