Yildirim had earlier been chosen by the ruling party as its new chairman, immediately vowing to make a priority out of implementing Erdogan's controversial plan for a presidential system to enshrine his status as the Turkish number one.
He replaces in both posts Ahmet Davutoglu, a former foreign minister who promoted his own ambitious agenda but threw in the towel after a power struggle with Erdogan.
In a carefully choreographed process, Davutoglu hours later met Erdogan at the presidential palace to formally submit his resignation as prime minister.
Yildirim then also went to the palace to be given the mandate to form the new government as premier, a presidential statement said.
Davutoglu will stay on as premier until a new government is formed but that should be in the next days.
By AKP convention, the posts of premier and ruling party chief are held by the same person.
"Turkey needs a new constitution. Are you ready to bring in a presidential system?" Yildirim said to cheers at the congress, saying this was the way to end the current "confusion".
Erdogan first came to power as prime minister in 2003, switching to the presidency in 2014. If he seeks a second presidential mandate in 2019, he could stay in power until 2024.
In a second speech after his election was confirmed, Yildirim added: "Our path is the path of Recep Tayyip Erdogan."
He is only the third party chairman in the history of the AKP -- which has transformed Turkey by putting Islam at the forefront of the officially secular country's politics -- after Erdogan and Davutoglu.
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