The 27-year-old singer and the 37-year-old actress and director - who met on the set of 'Don't Worry Darling' - were recently spotted on a yacht off the Italian coast and have also been staying in the five-star luxury boutique hotel in Porto Ercole.
Harry reportedly wanted to share his love of Tuscany - where he owns a home - with Olivia.
A source told the New York Post's Page Six: "Harry has a strong connection to Tuscany. He bought a small house there years ago when One Direction first became huge. It is no surprise he has brought Olivia here."
Meanwhile, it was recently claimed that Harry and Olivia - who has son Otis, six and daughter Daisy, four, with her former fiance Jason Sudeikis - have a “deep connection”.
An insider said: “It’s obvious that this was not a rebound or a short fling. They care so much about each other and have a deep connection.
“They’re pretty low key and have enjoyed being somewhat out of the public eye.”
And, separate insiders added that the couple have been “having an awesome time” together and have “grown even closer” since reports of their romance began swirling earlier this year.
The source explained in June: "[They are] having an awesome time. [They have] been going on walks outside in the park and not hiding their relationship, [and have] grown even closer as a couple.
"Yesterday, they enjoyed lunch outside and looked incredibly cute together. They were both in a great mood and left the restaurant holding hands. Harry put his arm around Olivia as they walked back to her house."
The pair were first reported to be dating in January after they were spotted holding hands while attending a wedding together.