TMZ reports that the 35-year-old LA Galaxy player is suing Nici and the magazine's publishers for $25m (£16m).
In his declaration, Beckham said that he has "never met Nici, let alone committed adultery with Nici or paid her for sex".
He added: "Irma Nici's statements have caused me and my family great anguish and emotional distress, and have adversely affected both my personal and professional life."
The original story, printed in early October, also accused the star of having a threesome and unprotected sex.
Beckham's rep told Us Weekly that the rumours were "totally ridiculous", adding: "Sadly we live in a world where a magazine can print lies and believe they can get away with it."
