Jonas filed the papers at the Miami Dade County Court on Tuesday, with reports saying they recently sold their house in the area.
However, in the papers obtained by NBC News, Sky’s US partner network, Jonas said their marriage is “irretrievably broken”.
He adds that the pair “have shared parental responsibility” over their children.
The filing also states they have a prenuptial agreement, and he has asked the court to uphold it.
Sky News has contacted representatives for both Jonas and Turner.
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Jonas is currently touring the US with his brothers in their group (Jonas Brothers), with reports saying he had his children with him on the road while Turner, who is best known for playing Sansa Stark in Game Of Thrones, is said to be filming in the UK.
News of a rift in their marriage emerged over the weekend, when TMZ said Jonas was lining up divorce lawyers.
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He has been spotted in recent weeks without his wedding ring, but he was wearing it during his show in Austin, Texas over the weekend.