But the new couple are expected to make their first official public outing together for a special family occasion – Pippa Middleton's wedding.
Kate Middleton's brother-in-law is expected to bring his American girlfriend as his plus one when Pippa marries James Matthews on May 20.
"Harry and Meghan are madly in love and he no longer wants to hide that from the world," a source said.
"He is close to Pippa and has been invited to her wedding and has obviously been given a plus one.
"Harry is adamant that he wants to take Meghan with him."
Earlier this week, the smitten royal and his TV star girlfriend were spotted walking hand-in-hand on a busy London street on Wednesday after enjoying a romantic dinner date at a private members' club in West London.