After starting out at Nacional, he spent the first part of his career in La Liga and went on acquire Spanish citizenship. He amassed league totals of 129 matches and 21 goals over seven seasons in the latter country, representing Getafe and Espanyol in the competition.
Other than Uruguay and Spain, Albín played professionally in Romania, Mexico and Cyprus.
On 21 April 2009, also against Real Madrid, Albín was struck in the face by Pepe, in the mêlée which resulted after the Portuguese's aggression on Javier Casquero.[5] He continued being used intermittently in 2010–11, netting a last-minute winner at home against Villarreal CF on 11 December 2010 but also being sent off for lifting his shirt, in a second bookable offence.[6]
Espanyol
In mid-April 2011, Getafe agreed to sell Albín to RCD Espanyol for €3 million, as his contract was set to expire in June 2012.[7] He spent several months of his first season on the sidelines, nursing a leg injury.[8]
Albín scored his first goal for the Catalans on 4 February 2012, netting in the 92nd minute for a 3–3 away draw against Athletic Bilbao.[9] In January 2013, due to lack of playing time, he was loaned to his former club Nacional.[10]
Later career
It's true that I came here for Contra, but I've found a great group [of players] and some incredible fans. [...] I want to stay.
— Albín on 15 March 2014, a few weeks before extending his contract with Petrolul[11]
On 6 September 2013, Albín signed a one-year contract with FC Petrolul Ploiești in Romania, rejoining his former Getafe teammate Cosmin Contra who was now a manager.[12] He made his Liga I debut on the 21st, scoring his team's goal in a 1–1 draw at FC Dinamo București.[13]
On 31 March 2014, Albín chose to extend his link by one year even if at that time Contra had already left.[14] He ended the campaign with 28 matches and ten goals in all competitions.
Albín returned to Romania and its top division nearly three years later, joining Dinamo București on a season-long loan with an option to buy.[17] On 18 July 2018, the 32-year-old joined Cypriot First Division club AC Omonia.[18]
Albín was a left-footed attacking midfielder who could also be deployed as a winger. He was described as a footballer with "great speed and a very good technique".[23]
During his first stint in Romania, Albín was known as an excellent free kick taker,[24][25] and in 2016 former international Adrian Mutu went as far to state that he was the best foreigner that the league ever had.[26]