"They are fully seeing each other," the source adds of the couple, who was first linked earlier this month.
The news of the pair's getaway comes the day after Hadid was spotted solo in Milan. Wearing a dark jumpsuit, white crop top and sunglasses, the model smiled, waved and signed autographs for fans as she was photographed in Italy.
Then, on Friday, Hadid stunned in an all-black look during the Versace Fashion Show.
DiCaprio, 47, and Hadid, 27, were first spotted in Casa Cipriani in New York City earlier this month.
"They were sitting in the dining room area and were canoodling and having a fun night out with each other," a source previously told ET. "... They are having a good time together and Leo is very attracted to Gigi."
Shortly thereafter, another source told ET that "Gigi and Leo are the real deal."
"They've been hanging out a lot and are very into each other," the source said. "Things are going well between them and they're both happy."
"Cami is upset because she saw a future with Leo, but she is fiercely independent and moving on," ET's source says.