Alice's family had asked for the scope of the inquest to include why Arnis Zalkalns was allowed to live unchecked in the UK.
The chief suspect who was jailed for murdering his wife in Latvia, Zalkalns was found hanged in west London.
Alice's parents said they welcomed the coroner's decision.
The full inquest, to be held in front of a jury, will start in June.
Alice, 14, went missing on 28 August last year having last been seen alive on the Grand Union Canal towpath near Hanwell.
Her body was found on 30 September after Scotland Yard's biggest search operation since the July 7 bombings in 2005.
Builder Zalkalns, 41, is believed to have killed Alice in a sexually motivated attack and then dumped her body.
He had been imprisoned in Latvia for murdering his wife but was released and travelled to the UK in 2007.
His body was found in woodland in Boston Manor Park.
Police said he would have been charged with Alice's murder had he lived.
Alice Gross investigation - timeline
The Gross family lawyer asked at a pre-hearing in October that the inquest should cover whether there was any failure by the authorities to implement statutory safeguards to protect the public under Article 2 of the European Convention on Human Rights - the right to life.
Sitting at the High Court earlier, Coroner Dr Fiona Wilcox said she accepted the submissions, adding that witnesses would be called to determine "how he (Zalkalns) came to be in the country in the first place, given his convictions for murder and firearms offences".
The inquest will also look at "the systems that were in place at the time, and whether appropriate checks were carried out".
Katerina Laiblova, Zalkalns' girlfriend, could be called to give evidence to the inquest about his mental state prior to his death, Dr Wilcox added.
In 2009 Zalkans was arrested on suspicion of sexually assaulting a teenage girl but no charges followed.
At the time of that alleged offence it appeared he was still subject to a supervisory or probationary arrangement in Latvia, that hearing was told.
A statement from Alice's parents, Ros Hodgkiss and Jose Gross, said they were pleased "at the range of information that the coroner is willing to put in front of the jury".
They also said it was their hope that the coroner "will be able to make recommendations to prevent this kind of thing happening again".
A further pre-inquest hearing is scheduled to taken place in April.
The inquest into the death of Alice Gross will examine whether failures by the government and police contributed to her death, a coroner has ruled.