Mr Asghari, 29, cited “irreconcilable differences” in a divorce petition filed in Los Angeles on Wednesday.
He asks that spousal support and payment of legal fees be paid by Ms Spears, the documents state.
Ms Spears, 41, said she was “a little shocked” that her six-year relationship with Mr Asghari had come to an end.
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Rumours of their marital struggles were reported in US tabloids this year. The two had recently been seen without their wedding rings in public.
In his own post on Instagram, Mr Asghari said: “After 6 years of love and commitment to each other my wife and I have decided to end our journey together.
“We will hold onto the love and respect we have for each other and I wish her the best always.”
He added: “Asking for privacy seems rediculous [sic] so I will just ask for everyone including media to be kind and thoughtful.”