Meeks and Chloe, whose father is worth £3.8billion, are believed to have met during the Cannes Film Festival in May this year.
The intimate yacht pictures show Jeremy gently holding onto Chloe's face, with the heavily inked catwalk star looking handsome in green board shorts as Chloe wrapped her arms around his muscular waist, with her wavy caramel locks flowing down her back.
The pair shared a moment looking into each other's eyes before moving their public display of affection to a deck chair.
There, they cosied up with Chloe shooting a seductive glance Jeremy's way as she reclined into his lap and puffed on a cigarette, while the model got within pecking distance of her lips.
Chloe and Jeremy's PDA-filled day didn't stop there as Chloe was seen with her leg wrapped around Jeremy as the pair looked wistfully out to sea.
Although surrounded by idyllic scenery on all sides, the pair only had eyes for one another as Jeremy affectionately fixed his ice blue peepers on Chloe.
Make-up free Chloe flaunted her radiant complexion as she stopped to take a quick photo.
The jailbird hunk then got to grips with the former shoe designer as he held onto her toned legs to give her a piggyback.
The display is somewhat surprising as Jeremy is married to wife Melissa, with whom he shares two children.
The chiselled star flaunted his honed midriff and numerous tattoos as he strolled about on deck before dive bombing into the sea.
Jeremy shared an envy inducing snap of him hanging out on the yacht to his 1.2m Instagram followers on Wednesday, with the caption Jim Jordan photography.
The snapper, who is known for women's fashion photography, is Jeremy's manager and his Instagram page is littered with photos of the former felon, suggesting Chloe and Jeremy may have been taking part in a highly convincing photo shoot.
Chloe's photos with Jeremy come as a source told The Sun: "Chloe seems quite taken with Jeremy, and who can blame her?
"He's seen as one of the sexiest guys on the celebrity social circuit and has a story or two to tell about his colourful past."
But the source added that Sir Phillip may not be quite as impressed, as he is "very protective".
"Quite what Chloe's dad and Jeremy's wife will make of their fling is another matter," they added.
MailOnline has contacted Jeremy's representative for comment
Both Jeremy and Chloe have separately been sharing sun-soaked snaps from the same location, both tagged with his manager, Jim Jordan photography.
And the snaps have garnered a mixed reaction, with one follower commenting: "He's dating Sir Philip Greens daughter Chloe. There are pictures of them making out on a yacht. One word dude, Karma."
But another defended him, adding:
Maybe they have broken up. Haven't seen neither of them post each other up on their pages for awhile. I doubt he would do anything in public if they were still together'
And tellingly, she replied "100"to a follower, who wrote: 'But the other person has to take value in you as well,why as woman we have to endure all the bullsh**?!You was with this n***a through jail time,broke times and all!How about you make him fight and endure some sh** like you have but nooo you you obviously bout to endure more pain for money!!Remember sister it's not worth it now you gotta deal with famous th*ts it will only get worse!".
The display comes after he mingled at an array of star-studded events during the Cannes Film Festival last month.
Meeks, whose looks have earned him a huge fanbase, made his first official modelling appearance at New York fashion week this year, and has certainly turned his life around in an impressive way since his release from prison.
However his journey to stardom hasn't been all smooth-sailing, after he was recently barred from entry to the UK after arriving at London's Heathrow airport from New York.
Speaking to DailyMail.com about the incident which prevented him from attending a work-related photoshoot, he said: "I'm very, very saddened and confused. I went down there [London] with high hopes for the experience and the UK.
"I really wanted to go there. I still don't understand quite what happened but I know there's no ill will. They're [Border Force] doing their job."
Asked what had happened to him, Jeremy, who described the incident as "a little mix up", said: "They just detained me and interrogated me and searched me."
But he also said he doesn't believe the episode will put an end to his fledgling modelling career, saying he planned to travel again: "Oh of course [I'll come back from this]. Of course. God is good."
The California native shot to fame in 2014 when the Stockton Police Department posted his mugshot on their website, following his arrest for gang activity and a misdemeanour charge of resisting/obstructing justice.
The photo promptly went viral, with internet users dubbing him "the hottest convict ever".
