The pair were spotted reclining and strolling on a beach in Florida this week.
The new couple stole a kiss, which was captured by paps at the scene.
The pair were also spotted together during New York Fashion Week last week.
Sofia, daughter of Lionel Richie, is fifteen years younger than her new beau.
Kourtney Kardashian, Scott's ex and mother to his three children, is reportedly embarrassed by his behaviour.
A source told The Sun: 'Kourtney is done with Scott – she finds his behaviour embarrassing.'
'She’s totally over it and can’t help but be furious with him. Why is he hanging around with teenage girls?'
Scott was previously linked to Bella Thorne, also 19, during the summer.
Kourtney has also moved on with a younger man. Her current boyfriend, Younes Bendjima is 23-years-old.