Kensington Palace had confirmed their relationship in November and they have met in various places around the world since then, including the prince's native London and Toronto, where she films Suits.
Meghan flew from the Canadian city to the British capital earlier this week to meet up with Harry again. A source told E! News the two have been "total homebodies" since she got to Kensington Palace.
"They've just been chilling at home," the source said. "There's always someone watching or trying to get pics when they go out that they're pretty happy just staying in and doing nothing. They like to cook, watch movies and that kind of thing."