The cabinet was unveiled after Erdogan took the oath of office for a second term as president with enhanced powers granted in last year's narrowly-won referendum.
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.
Earlier on Monday the lira briefly dropped more than 1 percent after a decree removed a clause stipulating a five-year term for the central bank governor.
The inauguration was to be followed by a lavish ceremony at his palace on Monday evening attended by dozens of world leaders marking the transition to the new executive presidency system. But he's also overseen a strong economy and he has built up considerable support across the country. A senior adviser to Erdogan later said that governors would still be appointed for a five-year term.
Ties with the United States and other North Atlantic Treaty Organisation partners also frayed, but Turkey remains crucial for any hope of stability in Syria and Iraq and curbing refugee flows to Europe. It later showed him visiting Ataturk's mausoleum in the capital, Ankara.
Erdogan will face immediate and major challenges in his second term, posed by an imbalanced fast-growing economy and foreign policy tensions between the West and Turkey, a North Atlantic Treaty Organisation member.
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.
In a ceremony at the presidential palace in Ankara on Monday, Erdogan named his cabinet, which includes loyalists, technocrats and business figures.
"Most powers will be concentrated in his hands, there will no longer be a prime minister, and nearly none of the checks and balances of liberal democracies will be present".
He then unveiled the first cabinet under the new system, appointing his son-in-law Berat Albayrak, 40, to the crucial post of finance minister, in a move that appeared to rattle markets.
The lira, which has lost almost a fifth of its value against the dollar this year, dropped almost 3 percent to 4.74 to the dollar minutes after the cabinet announcement. Investors are keen to see Mehmet Simsek, now deputy prime minister, continue at the helm of the economy. "In other words, Turkey will be an institutionalized autocracy".
In the aftermath of the 2016 coup, Turkey, a member of the North Atlantic Treaty Organisation military alliance and still nominally a candidate to join the European Union, has detained some 160,000 people, jailed journalists and shut down dozens of media outlets. It stood at 4.5655 against the dollar at 1508 GMT, strengthening slightly from Friday's close of 4.5745.
The currency has been battered by concern about Erdogan's drive for lower interest rates and comments he made in May saying he planned to take greater control of the economy after the June 24 elections.
Current Foreign Minister Mevlut Cavusoglu could, in theory, continue in his job but reports have said Erdogan may choose his spokesman, Ibrahim Kalin, or even spy chief Hakan Fidan to succeed him.
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.