In a statement Her Majesty and Prince Philip said they are 'delighted for the couple and wish them every happiness'.
Harry and his American fiancee, who divorced her first husband in 2013, will move into Nottingham Cottage in the grounds of Kensington Palace next door to his brother William and sister-in-law Kate.
The boys' father Prince Charles said he was 'thrilled' and 'very happy indeed' for them.
The TV couple's nuptials - which were postponed in season five - are understood to have taken place just weeks after the show's creator Aaron Korsh confirmed that Meghan's character would definitely be getting hitched to on-screen boyfriend Mike Ross in season seven. magazine reported that a film crew was spied in the King Edward Hotel in Toronto, and it's thought the actress wore the same £5,400 Anne Barge dress she first donned for the season five scenes.
The surprise appearance also sent fans into a frenzy of speculation.
One person said on Twitter: 'They are currently filming Suits in my hotel and I am freaking out!
Adams, co-stars Gabriel Macht and Sarah Rafferty were also on set.
Meghan's future on the television series has been the subject of debate, as she is reportedly set to leave once filming of the seventh season finishes next month, in order to pave the way for her wedding.