In another key change announced by Erdogan yesterday, army chief of staff General Hulusi Akar joins the government as defence minister but Mevlut Cavusoglu keeps the post of foreign minister.
Suleyman Soylu stays on as interior minister while Fuat Oktay, a former head of Turkey's emergencies agency, has been named as the sole vice president.
The appointment of finance minister had been keenly awaited by markets, with the naming of Albayrak, formerly energy minister, coming as something of a surprise.
The Turkish lira lost 2.4 per cent in value on the news to trade at 4.68 lira to the dollar.
The cabinet is the first named by Erdogan under a new system that dispenses with the office of prime minister and concentrates powers under the president.
Erdogan now sits at the top of a vertical power structure marked by a slimmed-down government with 16 ministries instead of 26 and multiple bodies reporting to him.
In one of the most significant changes, the EU affairs ministry, set up in 2011 to oversee Turkey's faltering bid to join the bloc, has been subsumed into the foreign ministry.
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