After his family moved to San Giovanni Rotondo, Conte attended the Classical Lyceum "Pietro Giannone" in nearby San Marco in Lamis and then studied Law at the La Sapienza University of Rome, where he graduated in 1988 with distinction.
Nakon što je njegova obitelj preselila u San Giovanni Rotondo, Conte je pohađao Klasičnu lice "Pietro Giannone" u obližnjem San Marco u Lamisu, a zatim studirao pravo na Sveučilištu u Rimu u La Sapienza, gdje je 1988. godine diplomirao s različitostima.