The 29-year-old prince has his eyes set on marrying Bonas and their friends said the wedding could happen soon, according to The Telegraph.
The friends said Bonas, 24, initially thought she was too young to marry Prince Harry but had finally overcome her fears about marrying into the royal family.
"Cressie is going to marry Harry," one of Bonas's friends told the newspaper.
"Harry never stops talking about marriage and children, and she has now got used to the idea. The wedding is likely to take place next year," the unnamed friend said.
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The prince was introduced to the British socialite in May 2012 by his cousin, Princess Eugenie of York, and was said to be "smitten".
Harry has previously said he has always wanted to have children, telling American talk show host Katie Couric he is looking for the right person to settle down with.
One of Bonas's friends said: "Cressida has been in floods of tears. Harry is coming on very strong, but she is all over the place. She thinks she is far too young to get married and is scared by all his talk of marriage and settling down."
On his return, the "romance blossomed, with nights at the cinema and time spent among friends", the report said. The pair have the "same sparkling sense of fun and relish a good party", it added.
Bonas studied dance at Leeds University and graduated from Trinity Laban Conservatoire earlier this year. Her family, which has direct links to Edward VII, is "bohemian and entertaining - something the Prince is said to like about them".