The newly engaged couple dished details about their engagement in an interview with the BBC ... revealing some pretty spectacular details about how it all went down. According to the couple ... the engagement happened a few weeks ago earlier this month at Harry's Nottingham Cottage inside Kensington Palace.

Harry got down on one knee and made his case ... but apparently a way-too-excited Meghan couldn't and wouldn't let him finish before charmingly butting in and asking, "Can I say yes now?" Adorbs.

And check this out ... Harry included 2 diamonds that belonged to his mother, Princess Diana, in Meghan's engagement ring "to make sure that she's with us on this crazy journey together."

Harry and Meghan met about a year and a half ago, but the relationship was turbocharged just 4 weeks into it ... when they headed to Botswana. Turns out, they never went more than 2 weeks without seeing each other. Completely fooled us.