Stemming from a civil society activism organization as the leader of MJAFT!, Veliaj joined the ranks of the Socialist Party of Albania in 2011, where he was appointed Secretary for Youth and Immigration.

[8] He attended the Sami Frashëri High School in Tirana and then later Grand Valley State University[9] in Allendale, Michigan where he graduated with a B.A.

Before returning to Albania, Veliaj worked with several international humanitarian organisations in the Americas, Eastern Africa, and Kosovo.

[11] On April 30, 2017, as Mayor of Tirana, Veliaj received “Doctor Honoris Causa” extended by the Grand Valley State University in the US for the contribution made in public services.

[13] Veliaj was one of the earliest activists of MJAFT!, a civic organization created in 2003 aimed at protesting social and political injustices in Albania.

[11] In 2004, ‘MJAFT!’ was granted the United Nations Award for Civil Society by Kofi Annan for its exemplary and highly efficient methods of protest.

[17] The center-left coalition of political parties won the 2013 Parliamentary Election and Veliaj was appointed to serve as Minister of Social Welfare and Youth in Edi Rama's new cabinet.

The candidate representing the oppositional Democratic Party was Halim Kosova, a well-known gynecologist, serving as a Member of Parliament at the time.

His death became controversial because the company that managed the landfill of Sharrë "3R", was promoted publicly by Veliaj himself as having good working conditions.

[26] On 27 November 2018, in a televised speech to the City Council, Veliaj reacted to the developing story about a police officer who lost her fingers in clashes with protesters in Tirana, by saying "We are all men here.

[30] This decision drew the widespread condemnation from several local activists, opposition political parties and artists against the Municipality of Tirana and the Albanian government.

[31] Several key people in the Municipality, all of them under the direct supervision of Veliaj, were implicated in a scandal surrounding the misappropriation of funds dedicated towards the garbage incineration plants of the city.

It was discovered that the city was severely overpaying for the plants, and officials in the central government and in local municipalities had conspired to grant the tenders for the operation of the incinerators to public-private partnerships which engaged in fraud.

[33] Five high-ranking directors in the Municipality were found to have conspired in creating a firm named 5D, to which several public tenders were granted.