Uriarte was born in Santiago on 17 July 1962, she was the only child of a lower middle class family. Uriarte became a mother when she was thirteen and her mother and grandmother had to support her. Her father died that same year. She says that the family savings were spent on buying her a caesarian operation She had to left her school because it was prohibited for teen mothers to continue studying, so she continued studying in a night school. After two years and when her son was old enought to be care in the day by her grandmother, she returned to high school in another area, where nobody knew her, hiding the fact that she was a teen mother. After a difficult time at school facing discrimination as a single and teen mother, Uriarte continued to succeed due to her hard work. She studied law at the University of Chile and worked part-time at the same time to support her family. She went on to be a student political activist during the 1980s building up the Student Federation of the University of Chile into an important organisation. She trained as a lawyer and was called to the bar in 1988 in Chile. When the Catholic church founded the Vicariate of Solidarity to support work in defence of human rights. She worked with Alfonso Insunza helping the victims of General Pinochet as a lawyer. Early in the 1990s she went to Germany for two years where her then husband was studying International law at Heidelberg University. Uriarte returned to the University of Chile where she became a Professor of Environmental Law. She taught on the Masters course in Environmental Law. She worked on a human rights programme for the government from 1993 to 2003. She became the Minister of the Environment for Chile in March 2007 and she served until March 2010 under President Michelle Bachelet. One of the controversies that was debated during her ministry was a proposal to dam rivers to flood land and create hydro electric power. She replaced by María Ignacia Benítez. In 2012 she was a partner in a Chilean Law firm still specialising in the Environment. She is currently a Professor of Environmental Law in the University of Chile