"Game of Thrones" star Madden, 33, was presented with the Most Stylish Man of the Year prize by singer Rita Ora, while Egerton landed the Actor of the Year honour from Sir Elton John's longtime songwriting collaborator Bernie Taupin.
Egerton portrayed the rocker in "Rocketman".
Rapper Stormzy was also a winner at the Tate Modern gallery, picking up the Solo Artist of the Year trophy for a second year.
Other winners included The 1975 (Band of the Year); Sir Ian McKellen (Legend of the Year); Kylie Minogue (Icon of the Year); revered crime author James Ellroy (Writer of the Year); Chinese activist Ai Weiwei (Artist of the Year), and David Beckham, who collected the Editor's Special Award from GQ's Dylan Jones.
Punk icon Iggy Pop was also recognised with a Lifetime Achievement Award.
See the full list of winners and presenters at the 2019 GQ Men of the Year Awards below: