The move comes ahead of an October 12 hearing in the Andrew Brunson case and amid growing expectations he will be allowed to return home.
Since July, Brunson has been under house arrest at his home in the western city of Izmir. Previously, he had been held in jail after being detained in October 2016.
His lawyer, Cem Halavurt, told AFP they would lodge the appeal in Ankara at 0700 GMT Wednesday.
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Brunson, an evangelical who runs a small evangelical Protestant church in Izmir, is the centre of a bitter standoff between the Turkey and the United States.
Washington imposed sanctions on Turkey over the summer and Ankara imposed sanctions of its own, leading to an escalation that prompted a crash in value of the Turkish lira.
The Turkish authorities detained Brunson on allegations of assisting groups branded as terrorist, part of a crackdown by the Turkish government following the failed coup in 2016.
But there have been signs the standoff could be easing.
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Last month, US Secretary of State Mike Pompeo expressed his hope Turkey would release the pastor.
Turkish President Recep Tayyip Erdogan said Monday Ankara hoped to rebuild relations with Washington, while adding that the pastor was on trial for his "murky relations with terror groups".
The easing of tension has helped the Turkish lira recover from historic lows in recent weeks.
Abdulkadir Selvi, a pro-government columnist for the Hurriyet daily, wrote Monday that the court on October 12 might rule to lift Brunson's house arrest and travel ban, allowing him to return home.
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