And fans could barely contain their excitement, with a video of the pair posted online notching up almost 23,000 likes and hundreds of comments.
Instagrammer belledbel wrote: "Please make babies," while katytaylor added, "I know harry is already dating a wonderfully beautiful girl but how about this for a perfect couple!"
Others commented on the 'cute' pairing with courtleigh8 calling them a
"match made in heaven".
Rihanna, 28, is rumoured to be newly-single after splitting from Canadian rapper and on-off boyfriend Drake, while Harry is well and truly taken.
Commenting beneath a video of the pair together on Kensington Palace's Instagram page, rieyelisa wrote: "Ummm yes I fully support this union."
Mallies went as far as saying they'd make "the cutest babies" with adore_echelon gushing: "You guys look stunning together oh my goshh."
One fan declared she would be "OK if they dated" while Pakittyy remarked: "RiRi Royalty!"
However not everyone was convinced, with twittyj blasting: "RiRi & Harry together? No thanks. She's a very talented lady, but not quite princess material. Pop princess, perhaps."
Harry met the songstress for the first time on Wednesday and it seems the pair became fast friends as, following their meet in the afternoon, enjoyed an evening at a concert together.
Rihanna joined the royal for a Golden Anniversary Spectacular Mega Concert at the Kensington Oval Cricket Ground the following evening.
Their visit marked the royal's tenth day of his two week official visit to the Caribbean.
With his visit to Barbados coming to an end Harry looked determined to make the most of his evening with the Diamonds singer.
The royal looked dapper in a pair of wine coloured chinos which he paired with a navy shirt for the event.
Harry is nearing the end of his 15-day tour of the Caribbean which has so far taken him to St Kitt's and Nevis, Grenada and St Lucia. He will finish in Guyana with a special visit to the country's President David Granger.
