Leicester boss has described as the “natural successor” to departed captain Kasper Schmeichel.
Schmeichel ended his 11-year stay with the Foxes earlier this week by joining Ligue 1 side Nice and Rodgers has appointed Northern Ireland defender Evans as his new skipper.
Evans will wear the armband when the Foxes launch their campaign at home against Brentford on Sunday.
Rodgers told a press conference: “Jonny represents the collective standards and values of these players and what they stand for. He’s a player of huge experience.
“He has huge respect in the changing room for what he’s achieved and how he behaves on a day-to-day basis. He’s the natural guy to step forward now Kasper has left.”
Former Manchester United centre-half Evans has made more than 100 league appearances for the Foxes since arriving from West Brom for £3.5million in 2018.
Rodgers paid tribute to Schmeichel, who joined Leicester from Leeds in 2011, describing the Denmark international as “a true icon of the club”.