"I don't have to sign players for the fans to pat us on the back, we're signing Phil because he is a good footballer and a great character to have around in our first season back in the Premier League," Wilder told the club's website.
"He has got a history with the club which is fantastic but meeting him and seeing his desire makes me delighted to see Jags back at home."
Jagielka, who has 40 England caps, made 385 appearances in all competitions for Everton, scoring 19 goals.
He was limited to seven league appearances last season after dropping down the pecking order as Marco Silva's side finished eighth in the league with 54 points.
"He's had a fantastic career, he was deserving of his move when we dropped out of the top flight last time and he went to a fantastic club and played all those games in the Premier League and captained England," said Wilder.
Sheffield United start their Premier League campaign at Bournemouth on Aug. 10.
(Reporting by Shrivathsa Sridhar in Bengaluru; editing by Clare Fallon)
