Under the new system, 64-year-old Erdogan will lead the state's executive branch and have the right to appoint and remove vice-presidents, a newly introduced position, as well as ministers, high-level officials and senior judges - without parliamentary approval.
Erdogan will face immediate challenges posed by an imbalanced if fast-growing economy and foreign policy tensions between the West and Turkey, a North Atlantic Treaty Organisation member.
Opponents say the new powers mark a lurch to authoritarianism, accusing Erdogan of eroding the secular institutions set up by modern Turkey's founder, Mustafa Kemal Ataturk, and driving it further from Western values on democracy and free speech.
Turkish President Tayyip Erdogan's son-in-law and newly appointed Treasury and Finance Minister Berat Albayrak (L) and Interior Minister Suleyman Soylu stand next to each other during a presser at the Presidential Palace in Ankara, Turkey July 9, 2018.
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.
Erdogan will this week immediately turn to foreign policy, visiting northern Cyprus and Azerbaijan followed by more challenging encounters at a North Atlantic Treaty Organisation summit in Brussels where he will meet his U.S. counterpart Donald Trump and other leaders.
The changes are the result of a bitterly fought referendum in 2017, where Mr Erdogan campaigned for a Yes vote and won narrowly amid allegations of vote rigging. The issue continues to polarise public opinion in Turkey.
But the pro-government daily Yeni Safak wrote under the headline "historic day": "One page is closing in Turkish history and a new page is opening".
In one of the most significant changes, the European Union affairs ministry, set up in 2011 to oversee Turkey's faltering bid to join the bloc, is being subsumed into the foreign ministry.
Crowds cheered Erdogan along his convoy's route as he made his way to the inauguration ceremony. Many independent and opposition news sources have been eliminated, and Turkey has become the world's biggest jailer of journalists. Foreign Minister Mevlut Cavusoglu remained in his post.
Among the dignitaries present at the ceremony were Venezuelan President Nicolas Maduro, Russian Prime Minister Dmitry Medvedev and Sudanese President Omar Hassan al-Bashir.
The markets were keeping a close eye on the finance ministry, keen to see a steady hand at the helm in a fast-growing economy dogged by double-digit inflation and a widening current account deficit.
The lira TRYTOM=D3, which has lost almost a fifth of its value against the dollar this year, dropped almost 3 percent to 4.74 to the USA currency after the cabinet announcement.
Investors were waiting to see whether cabinet appointees would include individuals seen as market-friendly, and particularly whether Mehmet Simsek, now deputy prime minister, would continue to oversee the economy.
His Justice and Development (AK) party and its ally the Nationalist Action party (MHP) hold a majority in the legislature.
Observers had speculated that the purge might ease after the elections, but on Sunday the government issued a decree dismissing 18,000 state employees including teachers, police and military officers over alleged links to terrorist groups.