Siblings Antony, 13, Angelina, 12, and Sienna Abdallah, 9, and their cousin Veronique Sakr, 11, were killed.
A fifth child was left in a critical condition and spent 80 days in hospital but survived. Two others were also injured.
Davidson's guilty pleas were indicated at his last court appearance on September 4, seven months after the crash that shocked a nation.
Clean-shaven and dressed in prison greens, he appeared calm when he flashed up briefly on screen before Parramatta Local Court on Thursday to confirm his admissions and be informed of his next court date.
"Hello," he said to Magistrate Peter Feather.
The charge of manslaughter carries a maximum jail term of 25 years in NSW.
The court heard the agreed facts of the case were still being ironed out and will be tendered to the District Court, where he will be sentenced.
The 30-year-old had ran a red light in the moments before the crash, having left a Caltex service station with a 24-year-old friend to return to his rented home on Greens Ave.
Davidson had MDMA and cocaine in his system and a blood alcohol reading of 0.15 – three times the legal limit – after his arrest.
The son of a retired police officer had been facing 34 charges, most of which were withdrawn on entering his guilty pleas.
Single counts of running a red light and not giving particulars to police will be taken into account on sentencing.
The Abdallah and Sakr families have both expressed forgiveness for the man who caused their worlds to crumble, and have consciously avoided his court appearances.
Last month father Danny Abdallah told the Daily Telegraph he would welcome Davidson's pleas but said it changed nothing for his family.
"It's not going to get our kids back, [but] the court [process] will be a lot quicker, so it will help us move forward," he said.
"Nothing's changed. How can I say it? Not a minute goes by not thinking about your kids. It's like it was yesterday, the pain remains and we're just trying to find a new normal in our family.
"We're determined to spend time with our children who are still with us and remain in constant prayer for the strength we need to see us through this time."
Davidson will be sentenced
on November 20.