With Rooney amongst the replacements, centre-back Gary Cahill will captain the Three Lions at Saint-Etienne’s Stade Geoffroy Guichard.
England need a win to be sure of finishing top of Group B.
Having come off the bench to score England’s goals in their 2-1 win over Wales, Vardy and Sturridge come in for Harry Kane and Raheem Sterling.
Jordan Henderson takes Dele Alli’s place in midfield while Jack Wilshire came in for Rooney alongside Eric Dier.
England manager Hodgson also opted to change both full-backs.
Nathaniel Clyde replaces Kyle Walker at right-back while Ryan Bertrand comes in for Danny Rose on the left.
Slovakia coach Jan Kozak has opted to keep faith with the starting side which beat Russia 2-1 last Thursday.
Slovakia (4-3-3)
Matus Kozacik; Peter Pekarik, Martin Skrtel (capt), Jan Durica, Tomas Hubocan; Juraj Kucka, Viktor Pecovsky, Marek Hamsik; Robert Mak, Ondrej Duda, Vladimir Weiss
Coach: Jan Kozak (SVK)
England (4-3-3)
Joe Hart; Nathaniel Clyne, Gary Cahill (capt), Chris Smalling, Ryan Bertrand; Jordan Henderson, Eric Dier, Jack Wilshire; Adam Lallana, Jamie Vardy, Daniel Sturridge
Coach: Roy Hodgson (ENG)
Referee: Carlos Velasco Carballo (ESP)
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