The 41-year-old activist made her name campaigning on poor families' doorsteps to protect them from eviction during Spain's recent economic crisis.
On Sunday she won the most votes in a municipal election, but faces a tricky job over coming days forging a coalition among a mixture of small rival parties who could unite to block her.
If she pulls it off, she could become the first of the new generation of “Indignado” (“Outraged”) protesters elected to a major public office – and the first woman mayor of the city.
Such a victory would take Colau inside the corridors of power that have so often been the target of her campaigns.
She ran for mayor at the head of Barcelona En Comu (Barcelona In Common), an alliance of grassroots groups including members of the left-wing party Podemos.
Opponents have branded her a mere populist or a dangerous radical and slammed her lack of experience.
But on Sunday more than 176,000 people voted for her.
“It is good for new people to get in, but they are very inexperienced and idealistic,” one voter in Barcelona on Sunday, Juli Montero, 54, said of Colau's party.
Another voter, Jordi Martinez, 36, said however that Colau's “lack of experience could be a good thing, a breath of fresh air in politics”.
Colau told AFP ahead of the elections that she wanted to make Barcelona “the spearhead of democratic change in Spain and southern Europe”.
Ending political privileges
Having risen to prominence as leader of the Platform for Mortgage Victims, Colau vowed her first measures if elected would be to defend poor families.
Authorities seized 95 homes a day in 2014 from inhabitants who defaulted on their mortgage payments, according to official data.
On top of that were countless other families evicted for defaulting on rent or for occupying vacant properties.
Colau proposes to turn empty homes into social housing, set a minimum monthly wage of €600 ($670) and make utility companies lower the price of gas, water and electricity.
With no experience of political office and no formal links to any established parties, she has vowed to do away with political “privileges”.
She promised to lower the mayoral salary to €2,200 a month if she herself takes the post.
The outgoing mayor, Xavier Trias of the conservative Catalan nationalist party CiU, earns €143,000 a year.
With short brown wavy hair, often in T-shirt and jeans, Colau has established a modest image.
She lives in a rented property with her partner, also an activist, and their four-year-old son.
Colau makes a point of travelling by public transport and has promised to reduce the use of official cars as mayor.
She has vowed to limit mayors to two terms in office.
Commitment to social justice
Colau studied philosophy but dropped out of university to work so she could help her family.
She worked in a series of low-paid jobs before joining a social research institute in 2007.
She says she has never earned more than €1,500 a month.
The fourth daughter of a graphic designer father and a sales representative mother, she was born on March 3rd, 1974 on the same day that the last prisoner of the Franco dictatorship, a Catalan activist, was executed.
“My mother reminds me of that every birthday,” she said. “That marked me in my commitment to fighting for social change.”
Her mother took Colau to her first protest demonstration at the age of five – the start of a lifelong habit.
She was active in student unions, anti-globalisation protests, demonstrations against the Iraq war and especially the campaign for housing rights.
Her anti-eviction group claims to have prevented more than 1,000 evictions.
It made Colau enemies in the governing Popular Party, one of whose members branded her a terrorist.
But it also earned her and the platform the European Parliament's European Citizens' Prize in 2013.