It is not yet known whether the family will join the duke for visits outside the capital.
Prince Harry had intended to travel with Meghan and their children, Archie and Lilibet, to attend celebrations marking the one-year countdown to the Invictus Games in Birmingham.
It has been four years since the children last saw their grandfather in person and the King has offered to put the family up at an unnamed royal residence.
There have been concerns over how they would be protected in the UK, amid reports last weekend that the prince’s request for taxpayer-funded police protection had recently been denied.
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