In February this year, the Sunday tabloid carried an interview with the couple's former nanny Becky Gauld, who made a number of accusations about their parenting skills.
Price and Andre appeared at London's High Court to accept the payment. The paper has retracted the claims made in the article.
"Anyone who has kids can imagine how they would feel to be accused publicly of being bad parents," Price told reporters outside court.
She added: "We came here today to see that justice was done and that our names were cleared."
The reality TV star declined to reveal the amount of damages they received from the newspaper.