The 46-year-old supermodel has been in embroiled in a battle which saw her ask for $46,000 per month from Hayek's current partner François-Henri Pinault.
Evangelista was due to take the stand in court on Monday (May 7). However, the New York Post reports that a deal was agreed before her appearance.
Although the terms are undisclosed, the matter appears to have been solved and both side are said to be happy with the result.
Pinault's lawyer David Aronson said outside the courthouse: "Everybody's glad for the sake and the benefit of the child that it's done."
Evangelista and billionaire businessman Pinault have 5-year-old son Augustin 'Augie' James together, while Pinault married his current wife - Puss In Boots actress Hayek - in 2009.
Hayek has a 4-year-old daughter named Valentina with her husband.
Pinault also has two older children from a previous marriage, which ended in divorce in 2004.
It was only revealed last year that he had fathered Evangelista's child, and a representative for the star had no comment to make on the outcome of the case.