Mr Yildirim, who is currently transport minister, is seen as a leading aide to President Recep Tayyip Erdogan.
Outgoing Prime Minister Ahmet Davutoglu had apparently objected to Mr Erdogan's plan to beef up his own power.
The president was known to be seeking a more "closely aligned" prime minister.
And, in a speech on Thursday, Mr Yildirim made clear he would work "in total harmony" with the president and all other levels of the AKP.
Mr Yildirim, 60, will be confirmed as the new leader of the AKP at an extraordinary party congress on Sunday. The party leader automatically takes on the role of prime minister.
Although Mr Erdogan's son-in-law, Energy Minister Berat Albayrak, had been mentioned as a possible candidate, his name did not feature among the top three men in a survey of MPs and party members.
President Erdogan is hoping to move Turkey from a parliamentary to a presidential system, with greater executive powers.
The choice of Binali Yildirim as frontrunner for the AKP's leadership has surprised few in Turkey, as he has been an Erdogan favourite for years. He has remained loyal in the most troubling times, and that loyalty appears to have paid off.
He has served as transport minister for many years, and did not hesitate to resign from his post to run for the mayoral elections in the western city of Izmir, a secular stronghold, at Mr Erdogan's request.
His name had come up as a possible candidate for the party leadership at last year's AKP congress. And that forced Mr Davutoglu to concede some of his powers within the party.
One AKP MP had to apologise after suggesting that the next prime minister would be a "low-profile" name. However, many in Turkey believe he will pose little threat to Mr Erdogan.
Among the reforms planned by the AKP is a proposal going before parliament on Friday to lift the immunity of MPs who are under investigation.
The measure is seen as targeting the pro-Kurdish Peoples' Democratic Party (HDP) as well as the main opposition Republican People's Party (CHP).
The HDP fears its 59 MPs could face prosecution and expulsion from parliament on charges of backing Kurdistan Workers' Party (PKK) militants. The large number of pro-Kurdish MPs in parliament has also hindered Mr Erdogan's aim of pushing through increased presidential powers.
A ceasefire between Turkey and the PKK ended weeks after elections in June 2015 and the renewed conflict has claimed hundreds of lives on both sides, particularly in Turkey's south-east.
Mr Erdogan has called for pro-Kurdish MPs to face terrorism charges and Friday's vote could be a first step towards making that happen.
If the government secures the support of 367 of parliament's 550 MPs, it will go through directly. If 330 MPs back the measure, then it could be put to a popular vote. A referendum is seen as more likely because 348 MPs supported the plan in a preliminary vote earlier this week.

Officers were called to the Ferry Road property at about 09:50 on Wednesday.
The baby boy was taken to the Royal Hospital for Sick Children in the city, where he died a short time later.
A Police Scotland spokesman, said: "Police in Edinburgh were called to Ferry Road around 9.50am on Wednesday October 12 following a report of concern for a nine-day-old baby."
He said: "The baby was taken to the sick kids hospital, where he was sadly pronounced dead a short time later.
"Inquiries into the full circumstances surrounding the death are ongoing and a report will be submitted to the procurator fiscal."
The death is being treated as unexplained.
The ruling AK Party in Turkey has picked Binali Yildirim as candidate for leader, a fortnight after a reported dispute with the president prompted the prime minister to quit.
[NEXT_CONCEPT]
A nine-day-old baby has died in hospital after police were called to an address in Edinburgh.