In the video the “Toxic” singer is seen showing off a four-carat diamond ring engraved with the word “lioness” – Asghari’s nickname for Spears.
It also shows Spears winking, kissing and smiling at her fiancé and answering “Yes!” when he asks if she likes the ring.
The 39-year-old captioned Sunday night’s post: “I can’t f***ing believe it.”
Asghari also posted a photograph of Spears showing off her ring finger to the camera on his profile.
The couple first met in October 2016 on the set of Spears’s “Slumber Party” music video.
The news comes four days after the Mississippi-born singer’s father Jamie filed a court petition to end the conservatorship arrangement that has controlled Spears’s finances and estate for more than a decade.
In June, Spears told a judge she wanted to marry Asghari and have a baby with him in an impassioned plea to end the conservatorship.
She said she had not been allowed to remove an intrauterine birth control device or even drive with him.
Spears can get legally married, but the conservatorship must approve this, as with other major life decisions she takes.
She was previously married to Kevin Federline, with whom she has two sons, aged 14 and 15, and was briefly married to childhood friend Jason Alexander in 2004.
Additional reporting from agencies