Born in Guatemala City, Colom studied at the El Rosario school, the Liceo Infantil and Costa Rica School, completing his secondary schooling at the prestigious Liceo Guatemala where he became student association president. He graduated as one of the top students. He entered the Law Faculty at the Universidad de San Carlos de Guatemala in 1950, again becoming a student leader there. He became involved in national campaigns for democracy and against the dictatorships during his studies and was one of 33 citizens to publicly oppose the 1954 plebiscite aimed at confirming Carlos Castillo Armas in power. He was targeted in the armed break-up of a student protest on 25 June 1956 which left several students dead.
Colom graduated as a lawyer and notary in 1957. He was granted a scholarship to continue his studies in Florence, Italy, having helped to found the Partido Revolucionario (Revolutionary Party), later leaving the party claiming it had abandoned its democratic ideals. He returned from Italy in 1960.
Back in Guatemala, Colom Argueta became involved in the '13 de Noviembre' movement backed by army officers against the government of Ydígoras Fuentes, soon leaving after differences over tactics. In 1961, he was one of the founders of the Unidad Revolucionaria Democrática (URD), which led opposition to Fuentes and Peralta Azurdia. In early 1962, students and workers rose up against the government; student and political leaders were sought. In the same year, he married an Italian, Anna Borghini, in Florence. Then together, returned to live in Guatemala and they had three children's (Anna Lorena, Monica and Manuel Rodolfo). On 25 January 1963, Colom and other leaders were detained, later forced into exile in El Salvador, where he worked at the National University.
In 1964, Colom Argueta was named Secretary General of the URD. In 1970, the URD, as the 'Civic Committee' proposed him as candidate for Mayor of Guatemala City, and he won the election comfortably. The Presidency was won by General Carlos Arana Osorio with Dr. Adolfo Mijangos López elected deputy for the Central District. Colom rolled out a wide municipal programme and worked as President of ANAM, the national association of Guatemalan municipalities. In 1973 he fought to have FURD – the Frente Unido Revolucionario Democrático – approved by the electoral commission so that it could fight the 1974 general election. The move was blocked by several delaying tactics, apparently as Colom would have had a good chance of winning the presidency. He was proposed as a candidate by members of other parties, but these moves were blocked by traditionalists. The opposition parties eventually backed Efraín Ríos Montt as candidate and claim to have won the elections. However, Kjell Laugerud García became President after alleged massive electoral fraud. Colom left for Europe.
In 1976, Colom Argueta returned and once again tried to form and register a political party – the Frente Unido de la Revolución (FUR). The same year there was an attempt on his life that left Colom injured and reliant on bodyguards after further attempts and threats. He continued his academic work at San Carlos University, combining this with politics.
On 15 March 1979, FUR was finally registered as a political party after several years. However, a week later on 22 March, Colom was assassinated by 36 gunshots, being the target of a carefully planned military operation lead by Major General Cancinos, that included army helicopters and several military resources (Cancinos was assassinated 3 months later). This assassination, under the military-dominated and repressive regime of General Fernando Romeo Lucas García (President 1978-1982), was one of several, including Social Democrat Party founder Alberto Fuentes Mohr.