Under the new presidential system Erdogan will have the power to dissolve Parliament, appoint or remove vice presidents, ministers, judges and high level officials as well as issue executive decrees and lift or impose a state of emergency.
He won last month's election with 52.6 per cent of the vote, ushered in the executive presidency that ends parliamentary governance and boosts the powers of the formerly ceremonial presidency.
The lira currency, which has been battered this year by concerns about President Tayyip Erdogan's drive for greater control over monetary policy, declined after the changes were published.
"We have come not to be master but to be servant of our people", he added.
It has also emerged that Mehmet Simsek, a former banker at Merrill Lynch who acted as deputy prime minister in Turkey's previous government, will not hold a position in the new cabinet. Foreign Minister Mevlut Cavusoglu remained in his post.
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 lira had on Monday lost over 3.5 percent in value against the dollar after Albayrak's appointment, with markets also rattled by changes to the president's relationship with the central bank under the new system that dispenses with the office of prime minister. The issue continues to polarize public opinion in Turkey.
Erdogan previously said that there will not be any members or parliamentarians of his Justice and Development Party (AK Party) in the new cabinet, hinting that it will be made up of ex-politicians and bureaucrats. Erdoĝan has repeatedly clashed with strategic allies such as the USA and the European Union in recent years over the war in Syria, Turkey's accession to the EU, human rights abuses by Ankara, Europe's failure to support Turkey during the coup attempt, and rising Islamophobia in Europe.
The post of prime minister will be scrapped. He is expected to become speaker of the new parliament. Few European leaders attended his inauguration - only those from Hungary and Bulgaria - with most from Africa and the Middle East: a sign of his geopolitical realignment.
Among the dignitaries present at the ceremony were Venezuelan President Nicolas Maduro, Russian Prime Minister Dmitry Medvedev and Sudanese President Omar Hassan al-Bashir. 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.
Prominent market-friendly ministers, who encouraged investor confidence, are not included in Erdogan's new government.
The markets will keep a close eye on economic appointments, 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, 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.
Ruhsar Pekcan, one of just two women in the cabinet, was named as trade minister.
Additionally, Turkish armed forces chief of staff General Hulusi Akar will be in charge of the defense ministry.
The AKP failed to win a majority in parliament, taking 294 of the 600 seats, meaning it will need its allies in the Nationalist Movement Party (MHP), which has 49 seats, to ensure a majority.