The move is widely believed to consolidate Erdogan's hold on power.
Transport and Communications Minister Binali Yildirim received 1,405 out of a total of 1,470 votes of delegates attending the governing Justice and Development Party, or AKP's, extraordinary congress.
The 60-year-old Yildirim, who is a founding member of the AKP, is now set to replace Prime Minister Ahmet Davutoglu, who announced earlier this month that he is stepping down amid differences with Erdogan.
Traditionally, the post of premier in Turkey goes to the leader of the largest party in parliament and Erdogan is expected to formally ask Yildirim to form a new government after the convention.
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In his speech before the vote Yildirim paid homage to Erdogan and expressed his devotion to him.
"We have always proudly said that we are Recep Tayyip Erdogan's companion, that we share a common fate and a common passion," Yildirim said.
He also vowed to work to introduce a new constitution changing Turkey's political system into a presidential system, to make the current "de facto situation" a "legal" one.
Earlier, in a message read at the opening of the convention, Erdogan again stressed the need for a new constitution and a new system of government and said he hoped the term ahead would help correct the current "skewed" system of administration. Delegates and party officials stood up as his message was read.
Supporters credit Yildirim for his role in developing major infrastructure projects which have helped buoy Turkey's economy and boost the party's popularity. But critics, including the leader of the main opposition party, have accused him of corruption. Yildirim has rejected the accusation.