Prince Harry, 33, explained to BBC's Mishal Husain that he proposed while they were cooking dinner at their cottage during a "cozy night."
"It was just an amazing surprise," Markle, 36, said. "It was so sweet and natural and very romantic. He got on one knee… I could barely let you finish proposing. I said, 'Can I say yes now?'"
Prince Harry added, "Then were were hugs and I had the ring in my hand and I was like 'Can I, can I give you the ring?' She goes, 'Oh yes the ring.' It was a really nice moment, it was just the two of us and I think managed to catch her by surprise as well."
The couple got engaged after a year and a half of dating. A mutual friend set them up on a "blind date."
Markle explained that she met Queen Elizabeth "a couple of times."
"It's incredible," she said. "To be able to meet her through his lens, not just with his honor and respect for her as the monarch, but the love that he has for her as his grandmother, all of those layers have been so important for me so that when I met her I had such a deep understanding and of course incredible respect for being able to have that time with her. She's an incredible woman."
As for the ring, Prince Harry explained he picked a yellow gold band because it is her "favorite." The main stone is from Botswana, where they vacationed, and the diamonds on the side are from his late mother Princess Diana's jewelry collection.
"I think everything about Harry's thoughtfulness is — and the inclusion of that and obviously not being able to meet his mom it's so important to me to — to know that she's a part of this with us."
The couple then discussed the challenges of their relationship, such as struggling with long distance.
"It was a choice," the Suits star said. "Very early on when we realized we were going to commit to each other we knew we had to invest the time and the energy and whatever it took to make that happen. With the filming schedule it was not the easiest."
Her future husband added, "I tried to warn you as much as possible, both of us were totally surprised by the reaction… you could have as many conversations as you want and try to prepare as much as possible, but we were unprepared for the scrutiny."
Markle then discussed race, as she was criticized for her ethnicity.
"Of course it's disheartening," she said. "It's a shame that is the climate in this world to focus so much on that. At the end of the day, I'm proud of who I am and where I came from. We have never put any focus on that we just focused on who we are as a couple. When you take all those extra layers away and all of that noise, I think it makes it really easy to enjoy being together and tune the rest of that out."
She added, "We were hit so hard in the beginning with a lot of mistruths that I made the choice to not read anything positive or negative. We focused all of our energy on our relationship."
Although Markle will be leaving her acting career, she will work more closely on her humanitarian efforts with her future husband.
"What's been really exciting is the transition of this out of my career and into the role of the causes that have been important to me," she said. "I can focus more energy on the causes I care about. I don't see it as giving anything up. I see it as a change. It's a new chapter. I've been working on my show for seven years. I'm very fortunate to be able to have that longevity on a series. Once we hit that 100 episode market I have ticked this box and I feel really proud of the work I have done there and now I can work on a team with you."
Prince Harry then explained that the couple hopes to start a family in the "near future."
The couple will tie in the knot in Spring 2018.
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