The pair, who had been dating for two years, ended their relationship amicably.
"It's very, very sad that they have decided to split. It's very amicable but they have decided to go their separate ways," the source said.
Cressida had been widely tipped to marry Harry, with speculation growing last month after she joined the Prince at one of his official engagements for the first time.
They sat together and embraced in the stands at Wembley Arena at a We Day UK charity event.
Kensington Palace declined to comment.
One of the reasons the couple decided to call time on their relationship was thought to be so that Cressida, 25, could concentrate on her career.
She completed a one-year contemporary dance course at the Trinity Laban Conservatoire in Greenwich, London, last year.
The pair, who headed off on a skiing trip together to Kazakhstan last month, are said to have been introduced by the Prince's cousin and Cressida's friend Princess Eugenie, although they have moved in the same upper class circles for a number of years.
They began dating about May 2012, reportedly getting together at The Valley festival on friend Arthur Landon's Hampshire estate.
They holidayed on Sir Richard Branson's Caribbean Necker island.