The couple has thanked their fans via twitter - with the cricket legend denying earlier reports that he had proposed in a crowded Scottish restaurant.
"I didn't propose in front of 200 people at dinner. It was done privately and was very romantic if I say so myself. Ps left knee is sore!!!"
Hurley was photographed Saturday wearing a sapphire and diamond ring, which reportedly cost Warne at least nearly $80,000.
They did not hide affection for one another on the historic golf course, where Warne earlier competed in a celebrity pro-am.
A spokeswoman for the championship said, "Shane is still out playing but he has confirmed his engagement to actress Liz Hurley."
Warne arrived in the UK early last week after spending time in New York City with Hurley, where she is filming the TV series "Gossip Girl."
They are set to visit the spin king's hometown of Melbourne later in the month. The couple has been dating for about 10 months after Warne split with wife Simone Callahan and Hurley with husband Arun Nayar.
Warne and Hurley first met at Britain's Goodwood races in July 2010 before publicly flirting on Twitter.
They were first reported to be an item after being photographed kissing in London in December last year.
Hurley has a son, Damian, from a previous relationship with entrepreneur Steve Bing, while Warne has three children with Callahan.