Erdogan, accompanied by his wife Emine, waves to supporters of his ruling Justice and Development Party (AKP) in Ankara early Monday.
Andalou said the party had won 42 percent of votes with 99 percent counted, projecting a total of 293 seats.
Turkish state news agency Anadolu, the only media distributing election results, reported that the Mr Erdogan easily claimed 52.7 per cent of the vote with more than 96 per cent of the ballots counted.
Mr Erdogan's main rival, Muharrem Ince of the Republican People's Party (CHP), conceded defeat but branded the elections "unjust" and said the presidential system that now takes effect was "very dangerous" because it would lead to one-man rule.
More than 56 million people were registered to vote at 180,000 ballot boxes across Turkey.
The expanded authority of the office is the result of constitutional changes narrowly approved in a referendum previous year, which will afford Erdogan autonomy to directly appoint top public officials.
Erdogan has however ruled out returning to a peace process with the separatist Kurdistan Workers' Party (PKK), which the UK, EU and Turkey deems a terrorist organisation. The lira has fallen more than 18% this year against the USA dollar as investors watched Erdogan attack the central bank's independence, suggesting that high interest rates stoke, rather than tame, inflation.
In a series of Twitter postings, Demirtas praised the party's success in winning a projected 67 seats out of 600, according to unofficial results.
"The restrictions we have seen on fundamental freedoms (due to the state of emergency) have had an impact on these elections", Ignacio Sanchez Amor, head of the OSCE observer mission, told a news conference.
Putin sent Erdogan a telegram to congratulate him on the victory, the Kremlin said in a statement Monday.
"Turkey is staging a democratic revolution", Erdogan told reporters in the polling station in Istanbul where he voted on June 24.
Erdogan's victory ensures he'll stay in office for 20 years - until 2023 - and ushers in a powerful new executive presidency that eliminates the prime minister's role.
"Voters had a genuine choice in the June 24 early presidential and parliamentary elections but the conditions for campaigning were not equal". Religiously observant Muslims form the bedrock of Erdogan's support.
Turkey has been under emergency rule, which restricts some personal freedoms and allows the government to bypass parliament with emergency decrees, for almost two years following an attempted military coup in July 2016. This brings the combined share of parliamentary power of the Justice and Development Party (AKP) and MHP to 53.6% - majority needed by Erdogan, who failed to win an outright majority in parliament. The report said they were not accredited to monitor the vote.
The CHP said it had recorded violations in the southeastern province of Sanliurfa. All we want is a fair competition. There are several problems to face: the decline of the Turkish lira, a massive 12 per cent rate of inflation and the perception that Erdogan is curtailing the central bank's independence.
With the promises made by opposition candidates during the election campaign, Erdoğan has also promised a prosperous new Turkey, a high-quality democracy where the rule of law would be the norm.
Recep Tayyip Erdogan has been elected as the first executive president of Turkey under the new presidential system.
As Turkey's democracy backslides, its European Union accession seems ever further away; however, Turkey will not want to lose European Union investment and trade and the West will not sacrifice the geostrategic importance of the country so relations, although perhaps strained, seem set to continue.