The pair were seen enjoying a date at the cinema this week, according to the latest news.
She then spent Harry's 30th birthday with him at Kensington Palace on Monday, adds the paper, before they enjoyed a date on Tuesday at the Odeon in Kensington High Street in West London.
The pair went to see the new Cameron Diaz and Jason Segel comedy Sex Tape. Harry was driven away by his bodyguards, and Cressida took a taxi in the direction of Kensington Palace, reports the Daily Telegraph.
A source told The Sun: "It's early days but Harry's over the moon. He realises she's the one for him."
Rumours had been swirling recently that Harry had started dating beauty queen Camilla Thurlow, 25, who has previously won the title of Miss Edinburgh. But it is believed that he has wanted to rekindle his romance with Cressida since she ended their two-year relationship back in April.
The source added: "Back in April, Harry was gutted, but determined to enjoy the summer. But despite him pursuing other girls, he realised Cress was the one."
So the question is: Do we need to buy a hat? Watch this space.
Just a few reasons why Cressida might love Harry (just like we do)...
And a lot of reasons why Harry fell for Cressie: