Those changes concentrate more power in the hands of the president.
Erdogan referred to the principles of Mustafa Kemal Ataturk, the founder of the modern Turkish Republic.
Parliament can ratify or reject his budget and the president needs parliamentary approval for emergency rule and decrees passed during that time.
The Turkish lira has weakened 16 percent against the dollar this year and capital has fled as Erdogan fought with his own central bank.
Erdogan's ruling Justice and Development Party (AKP) on Saturday nominated Yildirim as parliament speaker, an appointment likely to be rubber-stamped by the chamber on Thursday.
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.
"We, as Turkey and as the Turkish people, are making a new start here today", Erdogan said in an address late on Monday.
The inauguration in parliament after Erdogan's June election victory will be followed by a lavish ceremony at his palace attended by dozens of world leaders marking the transition to the new executive presidency system.
The decree also included the names of the newly appointed deputy president and ministers following President Erdoğan's announcement of the new Cabinet.
Ankara-President Recep Tayyip Erdogan Tuesday promoted Turkey´s army commander to overall armed forces chief in a radical military shake-up after the outgoing top general was given the post of defence minister. Foreign Minister Mevlut Cavusoglu remained in his post.
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. He also promised to "leave behind a system that cost the country heavily because of the political, social and economic chaos it caused in the past", according to Hurriyet Daily News.
On the eve of Monday's inauguration authorities dismissed more than 18,000 state employees - a lot of them from the police and army - in what the government said would be the final decree under emergency rule imposed following a failed 2016 coup. "In other words, Turkey will be an institutionalized autocracy", former EU Ambassador to Turkey Marc Pierini said.
"When you scrap the five-year term you remove this shield", he said. He was taken hostage during the night of the failed military coup in July 2016, which was blamed on US-based opposition cleric Fethullah Gulen.
Albayrak will be in charge of a new ministry of treasury and finance, replacing roles previously held by Deputy Prime Minister Mehmet Simsek, a former Merrill Lynch banker, and Finance Minister Naci Agbal.
Erdgoan has said he will announce the cabinet on Monday night, promising to make appointments from outside parliament and to slim down his ministerial team to 16 from more than 20.
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.