"They are both really excited and incredibly happy," a source told US Weekly magazine.
Nicky Hilton and James Rothschild
The source added: "They went on a romantic anniversary trip over the weekend.
"He took her out on a boat into the middle of Lake Como and he proposed, got down on one knee and everything. It was incredibly romantic and beautiful."
Nicky's older sister Paris also sent congratulations to Nicky and James over social media.
"Congratulations @NickyHilton on your engagement! I'm so happy for you! You will be the most beautiful bride! 👰 Such a lovely couple! Love you both so much! 😍" she captioned a blurry shot of Nicky and James posted on Instagram.
Could this be the boat where James Rothschild proposed to Nicky Hilton?
British banker James, who is based in London, is also thought to have flown to Los Angeles last month to get a blessing from Nicky's parents.
Nicky, 30, and James, who is a British banker, first met in 2011 at the wedding of Petra Ecclestone and James Stunt in Odescalchi castle, the spectacular 15th-century Italian fort where Tom Cruise and Katie Holmes also married.
They pair are now embarking on a road trip around Italy, which Nicky has been sharing on Instagram with her fans.
Nicky Hilton poses with a map on her Italian road trip
"Italian road trip begins!" Nicky captioned a shot taken last week of her in a convertible care with windblown hair, while a second snap was captioned: "Road trip continues.." showing Nicky reading a map.
She has also been posting pics of her view at Lake Como, delicious dishes of Italian pasta, and a boat trip.