The Prince is said to be besotted with Meghan after meeting in Toronto during the summer as Harry promoted his Invictus Games.
A source close to the Prince told The Express that while the romance is in its early stages, the royal is 'besotted' with the star, who plays Rachel Zane in the hit legal drama Suits.
The insider said that while they are taking things as they come and that Harry is anxious to shield the fledgling relationship from the public eye, the are loving each other's company and share a 'definite chemistry'.
The new couple are believed to have met in Toronto in May this year where LA-born Meghan is based and Suits is filmed.
Harry was in the city to promote his Invictus Games for wounded servicemen, and according to the source she's been to London to visit him on several occasions since.
Indeed, Meghan has shared two snaps of the capital - one taken nine weeks ago, and another 16 weeks ago.
In late June and early July she was seen enjoying the tennis from the royal box at Wimbledon.
She reportedly stayed at Kensington Palace during her time in London and has been introduced to the Duke and Duchess of Cambridge.
'William and Kate really liked her and she fitted in straight away,' added the insider.
As well as the pressure of dating a royal, Meghan may be eager to take things slow as she's already been married.
She wed her long-term boyfriend film producer Trevor Engelson in Jamaica in 2011, but the couple split three years later.
The same year she was also linked to golfer Rory McIlroy
Meghan caught the acting bug early and spent a great deal of her childhood on the set of Married With Children where her father was director of photography.
Her first gig was a role in the daytime soap General Hospital and roles in the sci-fi drama Fringe, 90210 and CSI: NY followed, before she got her big break with suits.
She's played the role of paralegal Rachel Zane since 2011.
Outside of acting, she's known for her philanthropic work, which is surely a big draw for Harry - especially given her interest in Africa.
Meghan caught the acting bug early and spent a great deal of her childhood on the set of Married With Children where her father was director of photography.
Her first gig was a role in the daytime soap General Hospital and roles in the sci-fi drama Fringe, 90210 and CSI: NY followed, before she got her big break with suits.
She's played the role of paralegal Rachel Zane since 2011.
Outside of acting, she's known for her philanthropic work, which is surely a big draw for Harry - especially given her interest in Africa.
A Senior Advisor to the Executive Director of UN Women got in touch and Meghan offered to fly to New York for work experience.
'I wanted to see what they were doing at ground level. It was important not just attach my name to an organisation, even if it was the UN,' she toldThe Aesthete.
'I called and said, "I have a week off from filming, can I come work in the office for a week?" They replied that no one had ever asked that.'
Meghan spent a week shadowing meetings dressed in work attire borrowed from the set of Suits.
Harry is said to be impressed by her energy and lust for life as well as sharing her interest in yoga.
The multi-talented actress has collaborated with Canadian fashion brand Reitmans on a clothing line, which goes on sale in the coming weeks.