The couple are set to remain in Germany until at least the weekend for Harry's 39th birthday before they attend the final celebration of the sporting event on Saturday.
Royal historian Tessa Dunlop claims the couple give each other gifts with "meaning" for their birthdays.
The Duke and Duchess are believed to be staying in Germany for Harry's birthday which falls on Friday - the day before the closing ceremony of the Invictus Games
She added that the Duchess is likely to try and make the day extra special for Harry as she knows it is a "difficult" time for him being so close to the anniversary of his mother and grandmother's death.
"I presume Meghan will join him there later, they'll do a double act there," she told OK! Magazine.
"They'll do something meaningful, they're in a neutral space in Germany and I think they'll have a good one.
"There's a lot of pain around a September birthday for Harry, because of the big funeral and the ramifications with his mother."
She told the crowd: "Hi everybody. It is so special to be here and I'm sorry I'm a little late to the party.
Meghan joined the Duke in Dusseldorf on Tuesday and was greeted by cheering crowds
"Like so many of you, you know this is about family and friends and the community that Invictus has created and Fisher House has created, and so I had to spend a little bit more time getting the little ones settled at home.
"Three milkshakes and a school drop off and I just landed a couple of hours ago and I am thrilled that the first event I can do for Invictus is here with all of you."
Meghan and Harry presented medals to participants as Queen's "We Are The Champions" was played throughout the arena.