Mitchell popped the question to Breeds in April as they shared a four-day break on Hayman Island, Queensland to celebrate his birthday. He had been preparing for the proposal for three months.
The pair, who play Summer Bay's Romeo Smith and Ruby Buckton, confirmed their news in the latest issue of New Idea magazine.
Mitchell told the publication: "Honestly, it was one of the most difficult things I've ever done in my life. I had the element of surprise - I didn't tell anyone what I was planning, not a soul, not even my parents.
"But pretending there was nothing special on my mind for three months before I actually asked her to marry me - that was the best acting I've ever done!"
Recalling the proposal, Breeds commented: "I turned around and there was Luke on one knee with a ring box in his hand. My jaw just hit the ground. I was so surprised I forgot to say 'yes' at first!"
The couple first met in May 2009 shortly after Mitchell had been cast in Home and Away. They initially became friends before embarking on a relationship.
Home and Away fans have also seen Romeo and Ruby have an on-off romance in the soap's storylines.
Breeds added: "I don't want a long engagement. There's a film out at the moment, The Five Year Engagement, but I don't think that's how we're going to roll!"
Home and Away airs weekdays at 6pm on Channel 5 in the UK and weekdays at 7pm on Network Seven in Australia.