The pair have been pictured holidaying together on a yacht in St Barts, sharing an intimate moment as they chatted on New Year's Eve before spending the first day of 2013 side-by-side.
The 25-year-old model was seen leaning into Dorsey, 36, and whispering something in his ear as he threw a party on Monday night.
Brainy pair: Lily Cole was seen cuddling up to her new beau Twitter founder Jack Dorsey
Captivated: The couple appeared to be in deep discussion as they chatted away on Monday night
Dorsey, whose personal wealth is estimated at $1.1billion, was pictured with Cole and other famous faces on a luxury yacht which is costing him a staggering $240,000 for a week.
New design: As well as showing off her new man, Lily has been flaunting her latest tattoo of a bird on the left hand side of her back
Making a splash: The Cambridge graduate was seen enjoying a dip in the water on Wednesday