On Sunday, the singer shared a video on Instagram of her wearing a diamond ring.
“I can’t f****** believe it”, she captioned the clip, alongside diamond ring emojis and a love heart.
In the the video, the 39-year-old star is seen showing off her ring, while the Iranian actor and fitness instructor asks if she is pleased with it.
“Yes!” she replies before planting a kiss on the 27-year-old’s cheek.
Britney, who met Sam on the set of her Slumber Party music video in 2016, recently praised her fiancé for his support during her “hardest years”.
Sam’s manager, Brandon Cohen, confirmed the engagement to People.
He said in a statement he is “proud to celebrate and confirm the engagement”.
He added: “The couple made their long-standing relationship official today and are deeply touched by the support, dedication and love expressed to them.”
New York City jewellers Forever Diamonds said on Instagram it designed the ring.
The jeweller showed a close-up of the silver sparkler, revealing the word “lioness” - Sam’s nickname for Britney - engraved on the inside of the ring.
A post on the Forever Diamonds Instagram page said Roman Malayev was the designer.
The statement said: “The thought and detail Sam put into this ring made the design process so special for Roman and our team. In honour of the Lioness herself, we are naming this gorgeous setting The Britney.
“Sam and Britney, we wish you a lifetime of happiness together and are honoured to welcome you to the Forever Diamonds Family.”
The engagement news comes after Britney’s father, Jamie, petitioned a court in Los Angeles to consider terminating her conservatorship.
The singer’s personal affairs and money have been controlled by a complex legal arrangement since 2008 after she suffered a series of mental breakdowns.
Britney had been demanding the conservatorship be brought to an end and accused her father of being abusive in his role overseeing her estate.
At a hearing in June, the singer alleged it was preventing her from marrying Sam and starting a family together.
During emotional testimony, she said: “I feel ganged up on and I feel bullied and I feel left out and alone. And I’m tired of feeling alone. I deserve to have the same rights, having a child or any of those things.”
In a stunning move last week, lawyers for Jamie, 69, filed to end the conservatorship. A judge will now have to approve the request.
Rumours began to swirl an engagement was in the offing after Sam was spotted at a jewellers in Beverly Hills.
Over the weekend he posted and then deleted a picture of the ring on Instagram and claimed he was hacked.
Sam is set to become the third husband of Spears.
She was married to backing dancer Kevin Federline from 2004-2007. He is the father of her 15-year-old sons Preston and Jayden.
Britney was also married to childhood friend Jason Alexander for 55 hours in 2004.
She was previously engaged to her former agent Jason Trawick in 2011, but they broke up in 2013.