Erdogan won an absolute majority in the presidential election on June 24 with 52.5% of the vote.
The post of prime minister has been scrapped and the president will now be able to select his own cabinet, regulate ministries and remove civil servants, all without parliamentary approval.
The main share index dropped more than 5 percent while bank stocks lost more than 9 percent in their worst day for five years as investors fretted over President Tayyip Erdogan's influence on monetary policy.
Since a failed coup attempt two years ago he's fired 125,000 workers, the latest 18,000 at the weekend, and jailed 160,000 people including opponents.
Just as Ataturk transformed an impoverished nation at the eastern edge of Europe into a secular, Western-facing republic, Erdogan has fought to bring Islamic values back into public life and lift millions of pious Turks - long ostracised by the secular elite - out of poverty.
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Meanwhile, President Erdogan hosted a dinner in honour of the delegations taking part in the inauguration ceremony, which was attended by Dr. Al Sunaidy.
Erdogan would become both the head of state and government, with the prime minister's post abolished.
Launching the executive presidency which he campaigned hard to secure, Erdogan also named a streamlined cabinet he says will push for growth to make Turkey one of the world's biggest economies. "Turkey is leaving behind a system which cost the country politically, socially and economically".
The new cabinet, due to be announced at 1800 GMT, is expected to have a different look, especially after Erdogan said the government would include non-AKP figures.
After the election victory, Erdogan removed Mehmet Simsek, previous deputy prime minister and a former Merrill Lynch banker, as well as former Finance Minister Naci Agbal.
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Marc Pierini, a former European Union ambassador to Turkey and visiting scholar at Carnegie Europe, said Erdogan's new powers effectively make him a "super-executive president".
Turkish President Tayyip Erdogan said that volatility in the dollar would decrease and that, when it comes to exchange and interest rates, domestic banks would lend support, local broadcasters quoted him as saying on Wednesday.
Erdogan, who has transformed Turkey by allowing Islam to play a greater role in public life and boosting the country's global stature, will take his oath nearly two years after defeating a bloody attempted coup.
He said Turkey would go further in every area in the new era, including democracy, fundamental rights, economy and large investments.
The state anthems of Turkey and Azerbaijan were played.
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Inflation surged last month above 15 percent, its highest level in more than a decade, despite interest rate hikes of 500 basis points by the central bank since April.