Maria Ladenburger, the daughter of a high-ranking EU official, was returning from a party in the university city of Freiburg in Germany when she was assaulted on a cycle path.
She was raped and then drowned before her body was found in the River Dreisam.
The shocking incident happened on October 16 but details have only been released after an arrest on Friday.
The suspect, an Afghan migrant, was caught after police found DNA on a scarf near the path.
The scarf reportedly belonged to Maria.
They also found a strand of hair on a nearby blackberry bush.
Officers then trawled CCTV to see find people with a similar hairstyle, which led them to the suspect.
Following his arrest the suspect, aged 17, pleaded guilty to the attack and will be sentenced next year.
The unnamed migrant arrived in Germany last year as an unaccompanied minor and lived with a local family in the city.
Ms Ladenburger reportedly worked in her spare time helping out in refugee homes in Freiburg.
But it is unclear whether she ever met her murderer before he took her life.
The dead girl's father is Dr. Clemens Ladenburger, a lawyer who works as the right hand man to the legal director of the European Commission.
On October 26 he and his wife Frederika placed a memorial notice for Maria in the Frankfurter Allgemeine newspaper.
It read: "Maria was for 19 years a singular ray of sunshine for our family, and that she will remain.
"We thank God for this gift, that he made you with us. We are sure that she is safe with him."
A funeral requiem was held for Maria on October in Notre Dame des Graces Church in Brussels.
On December 6 this year Maria would have been 20.
David Müller, head of the police's Special Commission, said: Through interviews and a web-based survey, we were able to reconstruct Maria's final hours.
Bundesrat President Stanislaw Tillich, German Chancellor Angela Merkel and German President Joachim Gauck (LtoR) arrive near Frauenkirche cathedral for celebrations marking the German Unification Day in Dresden, Germany, October 3, 2016
"The 19-year-old student had been at a party. By 2.37am, she left the party. Maria then cycled home, as usual. The young woman had been the victim of a sexual offence and a violent crime."
The horror killing piles more pressure on Chancellor Angela Merkel who opened the nation's borders to more than one million migrants since 2015.
Earlier this week she was blasted by a father-of-four who said he no longer felt safe because of the migrant inlux.
But Dieter Salomon, the mayor of Freiburg warned people not to "apply perpetrator background for sweeping judgements, but to view it as an isolated incident.
I notice the pro mass immigration media outlets like RTE, BBC, Guardian etc so far suppressing and ignoring this, also happening in Germany possibly to quel any "racist" backlash. Very sad, I don't think this will have any impact however. Knowing these sick Leftists they will probably apologise to the refugees. I'm afraid this is more blood on the hands of Angela Merkel, and this sickening stuff will be occurring in Ireland very soon. Sad this young woman tried to see the best in these people and paid for it with her life. RIP
Maria Ladenburger murder - EU official daughter killed by refugee | World | News | Daily Express
Teenage Afghan immigrant is arrested in Germany over murder of medical student | Daily Mail Online
Teenage refugee arrested on suspicion of rape and murder of 19-year-old daughter of senior EU official - Mirror Online