The couple were spotted enjoying a romantic holiday in The Caribbean, holding hands and sharing a tender kiss as they strolled along the beach.
Wearing a chic black bikini and a shell-adorned necklace, Emma put her arm around Matt, later embracing him as the pair swam in the sea together.
"They didn’t have a care in the world," a source told The Mirror. "Matt was very protective of Emma – often putting his arm around her."
"He was being a gentleman the whole time," added the source. "He is clearly very much into her. They couldn't stop giggling and smiling the whole time."
Reports that Emma and 21-year-old Matt were dating emerged earlier this week.
"It's early days but they're very much into each other," said a source. "Matt's a real hit with the girls, but he may have finally met his match.
"She doesn't suffer fools gladly. But Matt's a lovely guy, charismatic and intelligent. They make a great couple."
According to the newspaper, Emma's new man was the star of last month's Varsity win against the university's rivals Cambridge.
Matt, who is studying for a degree in languages, is considered to be one of Oxford's most eligible bachelors and was named best looking player on his team's Twitter account.
The news of Emma's new relationship comes shortly after her representatives confirmed that she had split from Will Adamowicz.