Quy Huy Hoang was sentenced in April 2016 to a maximum of 24 years in jail after being found guilty of 10 offences relating to five students.
His non-parole period was set at 18 years.
Hoang successfully appealed his convictions by taking his case to the High Court, which found that a juror engaged in misconduct by searching the internet for the requirements of a working with children check.
The 76-year-old faced a retrial before a judge in Sydney's Downing Centre District Court starting on September 19.
He pleaded not guilty to four counts of sexual intercourse with a child under 10 and four counts of indecent assault of a child under 16.
The charges related to four girls who were molested in their southwest Sydney homes between May 2011 and July 2014.
But on Monday he pleaded guilty to the rape charges.
The remaining counts of indecent assault of all four children will be taken into account by Judge Penelope Hock at a sentence hearing on December 13 in the District Court.
Hoang took efforts to isolate the children, convincing their mothers to have them tutored in separate rooms and to install things like locks and blackout curtains, the court had been told.
He was seen at the lessons with a black briefcase, which was filled with maths worksheets as well as vaseline, creams and lip-balm.
After seizing the case, police found one of the lip-balm containers contained a substance chemically identical to KY Jelly personal lubricant.
On his mobile phone, officers found a number of photographs of children, including the four victims.
Hoang was arrested at a Catholic church service in August 2014 after one of the girls' mothers reported him to police.
He is presently in custody.
1800 RESPECT (1800 737 732)
National Sexual Abuse and Redress Support Service 1800 211 028
