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Top-selling British tabloid The Sun told readers: "Harry is like a dog with a Bonas".
Photographs of the 28-year-old prince hugging the 24-year-old model and dance student graced the front page of every tabloid in England on Thursday.
The Daily Star labelled him "Flirty Harry".
The Daily Express's royal correspondent said Prince Harry had declared his love for Bonas "in an unprecedented public display of affection".
It would inevitably evoke memories of the first pictures of Prince William and Kate Middleton skiing together in Switzerland, the royal watcher wrote.
It's the first time Prince Harry has been spotted in such an embrace since splitting with former flame Chelsy Davy in 2010.
Prince Harry was first linked with Bonas in mid-2012.
But in August it was reported she'd dumped the third-in-line to the royal throne following his nude antics in Las Vegas.
Some suggested she felt humiliated following the release of naked pictures of Prince Harry partying with other women in Sin City.
Wednesday's ski-slope hug followed a more private display of affection at an up-market restaurant in the Swiss ski resort of Verbier.
"Cressida climbed on to Harry's knee," a fellow diner told The Sun.
"He started softly rubbing her hair then they began kissing.
"It was quite passionate - much more than a peck on the lips."
Prince Harry returned to Britain in late January after a 20-week deployment in Afghanistan in which he acknowledged he'd targeted Taliban fighters from the cockpit of his Apache attack helicopter.