Erdogan will meet Ghani, his first vice president Abdul Rashid Dostum, and his former poll rival Abdullah Abdullah, who took the new role of "chief executive", a Turkish official told AFP.
During his one-day tour Erdogan will also visit Turkish troops based in Afghanistan.
Ghani was sworn in as the new Afghan president in late September after a fraud-tainted election that had plunged Afghanistan into months of political deadlock and threatened to take it on the brink of civil war.
Turkey has refused to take on any combat missions in Afghanistan, fearing a Muslim backlash, with its troops primarily involved in providing security, reconstruction and training.
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Turkey has been cited as a potential mediator for negotiations between Kabul and the Taliban insurgents.
British Prime minister David Cameron visited Afghanistan early this month to hold talks with Ghani as NATO-led International troops end their long war against the Taliban.
NATO's follow-up mission, which will take over on January 1, will be made up of 9,800 US troops and about 3,000 soldiers from Germany, Italy and other member nations, among them Turkey.
The new mission -- named 'Resolute Support' -- will focus on supporting Afghan forces as they take on the militants, in parallel with US counter-terrorism operations.