Eliseu was born in Angra do Heroísmo, Azores to a Cape Verdean mother, Inês Furtado (a restaurant owner), and a Portuguese father, José (an ambulance driver).

[5] After a loan with Varzim S.C. in the Segunda Liga,[6] where he was banned for eight months after a positive doping test,[7] Eliseu continued to be a relatively important attacking player for Belenenses, but was used mainly as a substitute.

[13] After contributing to Zaragoza avoiding relegation – he also scored in the last fixture, a 35-yard free kick against the same opponents, in a 3–3 home draw[14]– Eliseu returned to La Rosaleda Stadium.

[16] Eliseu was a regular starter when available, netting in a 4–1 home win over Racing de Santander on 5 December 2010 from a volley and also providing two assists to Salomón Rondón.

[22] Eliseu made his official debut on 10 August 2014, playing the full 120 minutes as a left-back in a penalty shootout win against Rio Ave F.C.

[28] Already retired, Eliseu returned to the Estádio da Luz in May 2019 to celebrate the team's league win by driving around the pitch on his scooter, wearing sunglasses at night; he had marked the victory two years prior in the same way.

[29] Courtesy of his Málaga performances, Eliseu was first called to the Portugal national team for an exhibition game with Finland on 11 February 2009, but did not leave the bench.

He was selected by manager Fernando Santos for his Euro 2016 squad,[35] featuring against Hungary in the group stage (3–3)[36] and Poland in the quarter-finals (1–1, victory on penalties)[37] as the tournament ended in conquest.