Recep Tayyip Erdogan said voters had chosen stability following unrest.
With almost all ballots counted, state-run Anadolu news agency said the AKP had won 49.4% of the vote, with the main opposition CHP on 25.4%.
European observers have criticised the government for stifling media freedom.
The Organisation for Security and Cooperation in Europe (OSCE) said violence, especially in the country's south-east, had also had a significant impact on the election.
Meanwhile, the Parliamentary Assembly of the Council of Europe (PACE) went further and denounced the entire process as "unfair".
President Erdogan hailed the result early on Monday, saying: "The national will manifested itself on 1 November in favour of stability."
But he also attacked media criticism of him and called for global recognition of the election result.
"Now a party with some 50% [of the vote] in Turkey has attained power... This should be respected by the whole world, but I have not seen such maturity."
Gavin Hewitt: President's triumph leaves Turkey polarised
Erdogan: Turkey's bruised battler
Lira strengthens after result
Prime Minister Ahmet Davutoglu will now begin the process of forming a new government.
Mr Erdogan called the second general election this year after his AKP lost its parliamentary majority for the first time in 13 years in June and attempts to form a coalition failed.
The pro-Kurdish HDP crossed the 10% threshold needed to claim seats in parliament, but it got 21 fewer MPs than in June's election.
The nationalist MHP's share of the vote also declined, to 11.9%, and commentators suggested it had lost voters to the AKP.
Reported results also showed:
Clashes were reported in the mainly Kurdish city of Diyarbakir, in the south-east of Turkey, as the results were being counted. Reuters said police had fired tear gas at protesters throwing stones.
Since elections in June, a ceasefire between the Turkish army and militants from the Kurdistan Workers Party (PKK) has collapsed.
Critics have accused Mr Erdogan of renewing violence to curb support for the HDP - something the government denies.
In a statement on Monday, Ignacio Sanchez Amor, head of the OSCE observer mission, said: "Physical attacks on party members, as well as the significant security concerns, particularly in the south-east... imposed restrictions on the ability to campaign."
He added that pressure on journalists - including a police raid on the Koza-Ipek media group in Istanbul last week - was a major concern.
Meanwhile Andreas Gross, head of the PACE delegation, said: "Unfortunately, the campaign for these elections was characterised by unfairness and, to a serious degree, fear."
HDP co-chair Selahattin Demirtas said on Sunday that it had not been "a fair or equal election".
The party suspended campaigning after a bombing in Ankara last month killed more than 100 people. The government said the attackers were linked to the Islamic State (IS) group.
Violence has escalated in Turkey since a suicide bombing in July by suspected IS militants.
The attack near the border with Syria killed more than 30 Kurds.
Turkish newspaper front pages reflect the contrasting euphoria and gloom from government supporters and opponents at the election result.
"Ballot box revolution" declares Sabah, echoed by Aksam's "November revolution".
Pro-Islamist papers are equally jubilant, with Yeni Safak hailing a "magnificent victory", and Yeni Akit offering "congratulations to the Muslim world".
The independent mass-circulation Hurriyet and Milliyet focus on the scale of the ruling AKP's win.
Opposition papers accuse the authorities of scaring voters with the prospect of civil strife.
Cumhuriyet sees the "victory of fear", while the Sozcu tabloid thinks "terror has increased".
The left-wing daily Taraf accuses President Erdogan of using a "chaos plan" to whip up public insecurity, and the pro-Kurdish Ozgur Gundem predicts a "new era of struggle".
By BBC Monitoring
Turkey's president says the world must respect the results of the election, which saw the ruling Justice and Development Party (AKP) regain its parliamentary majority.