Violet Grace Youens died after Aidan McAteer's car struck her on Prescot Road, St Helens, Merseyside, on 24 March.
McAteer, 23, pleaded guilty to causing death by dangerous driving, during a hearing at Liverpool Crown Court. He is due to be sentenced on 19 May.
Violet's parents were in court, wearing violet ribbons in her memory.
McAteer also admitted causing serious injury to the girl's grandmother, Angela French, when his car struck her.
The 55-year-old is still recovering in hospital.
McAteer, who appeared via video link from Walton prison, sat with his head bowed throughout the 13-minute hearing speaking only to confirm his name and plea.
He had fled abroad after the crash, returning after a plea from his mother Alicia, who contacted police after seeing his photo on the internet.
At the same hearing, Dean Brennan, 27, from Prescot - who also appeared via videolink from HMP Liverpool - admitted aggravated vehicle taking and assisting an offender by providing McAteer with his passport.
He is also due to be sentenced next month.
Judge Dennis Watson QC said the importance of the case required the defendants to be produced in court.
Both men were further remanded in custody and the judge warned them to expect lengthy jail terms.
A man has admitted causing the death of a four-year-old girl who was hit by his car after it mounted a pavement.