After returning from his tour of the Caribbean and Brazil, the prince, 27, took his bags from his rooms at Clarence Houseover over to the Kensington Palace compound where Prince William and Kate live.
The prince is temporarily in a one-bedroom apartment in the Palace, until he can relocate to a bigger place when William and Kate move to their long-term home next year.
"This is not a huge space, but it is only natural now he's in his 20s that he would want to be independent and have his own place, and move out of the place he has been since he was a child," a Palace source tells PEOPLE.
"The princes are very close, and Harry is also very close to the duchess," the source adds. "They have all been thinking about this for a while, and when the opportunity came up they grabbed it."
It means that William and Kate and Harry can be geographically closer when they are all in London. "They do things privately together a lot," the source says, "and there are things that all three attend together in a formal capacity, and hopefully that won't change."
As previously announced, when William and Kate move into their permanent home, Apartment 1a, late next year, Harry will move into their two-bedroom home, Nottingham Cottage. Work on their home begins in earnest in September.