The singer posted a video of the couple showing off the ring on Instagram.
The 39-year-old is fighting a legal battle to end her 13-year conservatorship, which controls both her personal life and finances.
Spears has revealed that the terms of the arrangement are preventing her from marrying Mr Asghari, 27, or having more children.
The conservatorship arrangement was imposed in 2008 when concerns were raised over her mental health.
Last week, her father, Jamie Spears, filed papers in a Los Angeles court to end the conservatorship. A court hearing is scheduled for 29 September.
Mr Asghari, an actor and fitness trainer, posted a separate photo of the ring and the couple kissing.
His manager, Brandon Cohen, confirmed news of the engagement to People magazine.
"The couple made their long-standing relationship official today and are deeply touched by the support, dedication and love expressed to them," he said.
The couple met on the set of a music video in 2016.