The lira, which has lost almost a fifth of its value against the dollar this year, dropped almost 3 per cent to 4.74 to the USA currency after the cabinet announcement.
The appointment of Berat Albayrak appeared to rattle the markets amid concerns of nepotism in the upper echelons of power.
Erdogan, as AK Party chair, won a great victory in the July 2007 general elections, and established Turkey's 60th government by winning 46.6 percent of the vote as well as a vote of confidence. Reuters adds: After taking the oath of office in parliament, he addressed global leaders gathered at the presidential palace in Ankara.
"We as Turkey, and the Turkish nation, are making a new start here in your presence".
Launching the executive presidency which he campaigned hard to secure, Erdogan will also name a streamlined cabinet he says will push for growth to make Turkey one of the world's biggest economies.
For 95 years, Turkey was a parliamentary republic, its Grand National Assembly the heart of power.
"In the coming period we will work intensively to bring inflation down to single digits", Albayrak said at a handover ceremony with Simsek, whose post no longer exists in the new government.
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That was despite the likes of Mr Johnson and Mr Davis privately expressing their reservations about the prime minister's strategy. Other pro-Brexit Cabinet ministers said they supported May and would not resign.
The post of prime minister will be scrapped. But he's also overseen a strong economy and he has built up considerable support across the country.
Foreign minister Mevlut Cavusoglu, who kept his position in the new cabinet, said he wanted Turkey to continue its bid to join the European Union, Hurriyet Daily News reported on Tuesday.
Erdogan, the most popular and divisive leader in recent Turkish history, has now formally become the most powerful leader since Mustafa Kemal Ataturk founded the republic from the ruins of the Ottoman empire. "In other words, Turkey will be an institutionalized autocracy".
Under controversial constitutional reforms approved by a referendum previous year, parliament has been weakened and the post of prime minister abolished.
The country has been under a state of emergency for nearly two years since the failed 2016 coup, but Erdogan said he would end it after the election. The lira, which gained more than 1 percent earlier on Monday to 4.51 against the dollar, briefly fell back sharply after a government decree removed a clause stipulating a five-year term for the central bank governor.
"The central bank will not have independence, there will be no restraints on the president in determining the budget [and] spending priorities", said Kuran.
"The pace at which he (Erdogan) is moving to tighten his grip is alarming and, in response, Turkish financial assets have come under pressure", said Jason Tuvey, senior emerging markets economist at Capital Economics, in a note to clients.