Critics have long denounced the move as part of a grab by Erdogan for one-man rule, but supporters say it simply puts Turkey in line with France and the United States and is needed for efficient government.
Erdogan hailed a "historic decision" after unofficial results showed a narrow 51-49 win for the 'Yes' camp but the opposition immediately vowed to challenge the outcome, alleging violations.
He has denounced as "lies" opposition claims that parliament would be neutralised and the judiciary would come under his political authority after the changes.
What will change in the new 18-article constitution for the nation of 79 million people, which will replace the current document adopted in 1982 after the 1980 military coup?
More powers for President Erdogan
The president would have strengthened executive powers to appoint top public officials including ministers directly.
The president would also be able to assign one or several vice presidents. The office and position of prime minister, currently held by Binali Yildirim, would be scrapped.
There would be a shake-up in the judiciary, which Erdogan has accused of being influenced by supporters of his ally-turned-foe, the US-based Islamic preacher Fethullah Gulen.
Gulen is blamed for the July failed military coup against Erdogan but denies the government's accusations.
The president and parliament would together be able to choose four members of the Supreme Board of Judges and Prosecutors (HSYK), a key judicial council that appoints and removes personnel in the judiciary.
Parliament will choose seven members on its own in what would be renamed the Board of Judges and Prosecutors (HSK).
Military courts, which have convicted officers and even sentenced former prime minister Adnan Menderes to death following the 1960 coup, would be banned.
Longer state of emergency
A state of emergency would be imposed in the event of an "uprising against the homeland" or "acts of violence which put the nation in... danger of being divided".
Initially the emergency would last six months -- as opposed to three now -- then it could be extended by parliament after a presidential request for four months at a time.
Turkey has twice extended the current state of emergency imposed after the July 15 coup bid.
President Erdogan can rejoin AKP
The number of members of parliament will rise to 600 from 550 while the minimum age limit for MPs will also be lowered to 18 from 25.
Legislative elections would take place once every five years -- instead of four -- and on the same day as the presidential poll.
Parliament will still have power to enact, modify and remove legislation. If the president were accused or suspected of a crime, then parliament could request an investigation.
The president will also have to be a Turkish citizen aged at least 40, and can be a member of a political party.
Currently the president must be impartial and without party favour, although opponents have accused Erdogan of blatantly flouting this rule.
The change will again allow Erdogan to become leader of the ruling Justice and Development Party (AKP) that he co-founded.
President Erdogan in power to 2029?
Erdogan was elected president in August 2014 after more than a decade as prime minister, in the first ever direct election for a Turkish head of state.
The new constitution states that the next presidential and parliamentary elections are to be held simultaneously on November 3, 2019.
The president would have a maximum of two five-year terms -- so Erdogan could stay in power for another two terms until 2029.