The 58-year-old actor confirmed the news on live TV on the Oscars red carpet on Sunday evening, casually making the announcement mid-sentence during an interview about 'Get Out', the acclaimed horror movie in which he plays Dean Armitage.
Speaking to E! News' Ryan Seacrest at the awards bash in Los Angeles, he shared: "I walked out of the room and I said to my fiance, this is unlike any script I've ever read. This could be incredibly brilliant or it could really not work."
Bradley's representative subsequently confirmed the news to the American broadcaster.
Rumours about their engagement started circulating on Friday at the 11th Annual Celebration of the 2018 Female Oscar Nominees in Beverly Hills, where the actress - who plays Sarah Pfefferman in 'Transparent' - was spotted wearing a ring on her engagement finger.
Bradley joined the cast of the award-winning Amazon series in 2014 and the celebrity couple confirmed they were dating the next year.
Bradley previously said of their romance: "Things with Amy are spectacular. Things are wonderful."
However, Amy previously admitted that she took a while to be convinced that Bradley was a suitable romantic partner for her.
The 48-year-old star initially considered her future husband to be a "cocky actor boy", adding that she didn't consider dating him at the time.
She confessed: "I knew Bradley for a year before we dated and I kind of thought that he seemed like a cocky actor boy and I wasn't really that interested.
"Now I've learned that If I don't like someone at first, that's probably a sign that they're perfect for me because my taste is so bad ... so I was like, 'Oh, see here it is!' I didn't think and now I'm the happiest I've ever been."