The French beauty firm's luxury products division already makes fragrances and cosmetics for Armani and Saint Laurent as well as its own labels such as Lancôme.
It is competing with US cosmetics group Coty which became the world's leading perfume producer by buying Procter & Gamble's beauty division in 2015, and also has licences for brands like Gucci and Hugo Boss.
"L'Oréal aims to become the world leader in perfumes. This license should allow us to reach that goal," a spokeswoman said.
L'Oréal did not disclose the terms of the agreement, which will become effective from 2019, after regulatory approvals. The contract with Puig was due to expire at the end of 2018.
By Pascale Denis and Sarah White; editor: Alexander Smith.
Editor's Note: This article was revised on 29 May, 2018. A previous version of this article misstated that Coty owns the fragrance licence for Dolce & Gabbana. This is incorrect. Shiseido Group owns the fragrance licence for Dolce & Gabbana.