President Erdogan said Wednesday the elections will take place on June 24 of this year, instead of in November 2019.
A referendum on an 18-article bill itemizing the switch was approved by voters in April 2017.
The enhanced powers of the presidency will take effect after the June elections.
The eagerly-awaited meeting between Erdogan and Bahceli started at 1030 GMT lasted only half an hour, the presidency said, without giving further detail.
But Erdogan's military incursions into Syria, where Turkey is battling Kurdish fighters, have boosted his popularity, and analysts said the president hopes to ride that wave of support to an election victory.
"The government has welcomed [Nationalist Movement Party leader Devlet] Bahceli's idea to hold early elections".
The snap elections are a key test for Erdogan's Justice and Development Party (AKP), which despite holding a parliamentary majority, faces challenges that could erode its popularity.More news: Russian Federation 'complicit' in Syrian regime's retention of chemical weapons: Mattis
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The polls will also give Erdogan a chance to extend his stay in power with a new-five year mandate, after already serving 15 years in power as premier and then president.
Bahceli argued that there is "no point in prolonging this any longer", citing efforts by unnamed groups to foment chaos in Turkey.
The new rules will mean the Turkish president is head of state, head of government, and head of the ruling party.
The European Union, which Ankara seeks to join, said in a report published on Tuesday that measures undertaken by Turkey under the nearly two-year-old state of emergency have curtailed civil and political rights and called for its immediate lifting. "The country needs to brought out of the emergency rule regime starting today", Republican People's Party (CHP) spokesman Bulent Tezcan said.
The European Union, the body for which Turkey seeks membership, has called on the country to end its emergency rule, saying that it has resulted in human rights violations such as torture and arbitrary detention.
The principal opposition party accuses the government of misusing its emergency forces to erode politics and arrest government leaders.
Turkey declared a state of emergency for the first time on July 20, 2016 following a deadly coup attempt by Fetullah Terrorist Organization (FETO).