This means they have beaten a world record, by almost six hours.
The fastest time to gain one million followers was achieved by K-pop star Kang Daniels, who gained a million followers in 11 hours and 36 minutes, according to the Guinness World Records.
At time of writing, Meghan and Harry now have 2.1 million followers.
Meanwhile, the most-followed Instagram account in the world is currently Instagram itself, followed by footballer Cristiano Ronaldo.
As for other Instagram records, the Guinness World Record for the most-liked post on the platform is currently held by an egg – although who knows whether Meghan and Harry may be able to break this record in the future, too.
The royal pair have shared just one post so far: a gallery of images which features their solo and joint engagements since their engagement announcement in November 2017. It has gained 743,000 ‘likes’ at time of writing.
The new platform has been established ahead of the birth of the couple’s first child, expected at the end of April.
Last month it was announced that Meghan and Harry have created their own royal household, which will be based at Buckingham Palace.
This is a move away from the Duke and Duchess of Cambridge’s office, which will continue to be based at Kensington Palace.