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.
However, prosecutors say he can still change his plea and it’s unknown if he has admitted raping Maria.
The unnamed migrant arrived in Germany last year as an unaccompanied minor and lived with a local family in the city.
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.
The teen worked voluntarily at a migrant centre
Maria’s father works at the European Commission
“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.
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”.
However, police are also investigating whether the murder of Maria is linked to another killing just a month later.
Carolin Gruber was sexually assaulted and murdered in an attack at the same spot.
The 27-year-old was found in woodland elsewhere in the city on Novermber 10.