Flamurtari Vlorë He made his debut for
Flamurtari Vlorë in 2006 and since then has cemented his place in his hometown club's first team. He has spent most of his career in the left back position but he has also played as a left midfielder and most recently as a central defender as well. On 29 October 2008, he scored his first hat-trick, an unusual achievement for a defender, in a 1–6 away win against
Naftëtari Kuçovë valid for the first leg of the first round of
2008–09 Albanian Cup. He was voted Flamurtari's player of the year for 2014 by the club's fans, beating
Bruno Telushi and
Ardit Shehaj who came second and third respectively.
Kukësi After making 263 appearances for Flamurtari between 2006 and 2015, Veliu left to join fellow
Albanian Superliga club
Kukësi.
Partizani Tirana On 1 February 2016, Veliu joined
Partizani Tirana where he signed a contract until the end of the season with an option to extend it for a further year. After some matches in bench, Veliu made his first appearance with
Red Bulls on 20 March by playing in the last 13 minutes of a 0–2 win at
Teuta Durrës. He played his first match as starter later on 17 April in the 3–0 home win over
Vllaznia Shkodër; he was however replace at the end of first half. Veliu left the club following the end of the season after making only three appearances, collecting only 80 minutes as the team finished runner-up in the championship.
Return to Flamurtari Vlorë On 22 July 2016, Veliu officially returned to
Flamurtari Vlorë by joining as a free agent. He was allocated his old squad number 11, and made his return debut on 7 September in the opening league match of the season, a 2–1 away defeat to
Skënderbeu Korçë. On 27 May, in the final matchday, Veliu scored his first goal of the season after an individual effort in a 3–0 win over
Korabi Peshkopi, as Flamurtari avoided the relegation by just one point. In June, following the departure of team captain
Bruno Telushi in Croatia, Veliu was renamed the new captain, three years after losing the status. He suffered a major injury during the summer preparation phase which forced him to miss the entire first half of 2017–18 season. On 22 July 2017, Veliu signed a contract running until July 2018. He returned on action in the first days of January 2018 where he played in a friendly against the under-19 side.
Gjilani In summer 2019, Veliu moved abroad to play for
Football Superleague of Kosovo side
Gjilani. ==International career==