Born in Tirana, Albania Gjasula started his career in the town where he grew up at SC Freiburg in Germany in 2002. At the age of 17 he was put into the first team but did not make any appearances.
Gjasula signed for 1. FC Kaiserslautern in 2004 and made it a total of seven appearances in one season.
In 2005, Gjasula was loaned in club FC St. Gallen on Swiss Super League. At first season with St Gallen, he became a box-to-box goalscoring threat and typical number 10 so he signed a contract in 2006.
Gjasula signed for Swiss Champions FC Basel as a free agent on 2 June 2008. He scored his first goal for FC Basel on 10 July 2008 in a 6–1 win over Legia Warsaw in the Uhren Cup and made his competitive Basel debut on 18 July 2008, in a 2–1 win over BSC Young Boys at the Stade de Suisse, Wankdorf. He played his first European game in a Basel shirt on 30 July 2008 in a 1–1 Champions League Qualifying match draw against IFK Göteborg at Ullevi. On 18 June 2009, he was released by Basel after newly appointed manager Thorsten Fink decided not to offer him a new contract
Gjasula signed on 31 August 2009 for FSV Frankfurt where he made it a total of 60 appearances and scored nine goals in two seasons with club.
In July 2011, he signed for MSV Duisburg.
On 5 July 2013, Gjasula signed with Bulgarian club Litex Lovech, rejoining his compatriot and fellow Albanian international player Armando Vajushi. He quickly established himself as a crucial player in the squad, providing several goals for the surprisingly magnificent start of the club.
Gjasula scored the third goal from the penalty spot in the 2–4 away victory on 20 October 2013 against a hard opponent such as Ludogorets Razgrad. A week later, on 27 October, Gjasula scored the second goal in the 90th minute of the 0–2 victory over Neftochimic Burgas.
Litex finished first stage of the 2013–14 season as runners-up, where they had last match of 9 March 2014 against winners of the league Ludogorets Razgrad and they were only 1 point difference and match between them finished as a 0–0 draw. For the regular season Gjasula made 26 appearances including 3 in the Bulgarian Cup, 11 goals were 9 scored in the league, positioning in 8th place on League's rank of Top scorers and 2 goals scored in Bulgarian Cup, also 8 assists positioning in 4th place on League's rank of Top assists.
Gjasula finished the 2013–2014 season scoring in total 11 goals (including 2 in the Bulgarian Cup) in 35 appearances and Litex ranked 3rd in the league table, gaining entry to play in the UEFA Europa League for the next season.
With coming of the new coach Miodrag Ješić, Gjasula wasn't anymore in the club planes as they announced that will not renewing him the one-year contract that he had. On 4 June 2014, Turkish side Bursaspor announced that they were looking for an Offensive midfielder and the 28-year-old Gjasula is an option.
On 10 September 2014, Gjasula signed with 2. Bundesliga side VfR Aalen a contract until June 2015.
On 7 June 2015, it was announced, that Gjasula had signed a contract with Greuther Fürth.
Gjasula decided to play for Albania national football team in May 2013. He received an Albanian passport on 24 May 2013 among other compatriots, Amir Abrashi, Vullnet Basha, Azdren Llullaku and Ilir Berisha and so he was able to play on international games. He received his first call-up by coach Gianni De Biasi for 2 matches against Norway on 22 March 2013, valid for the 2014 FIFA World Cup qualification and the friendly against Lithuania on 26 March 2013. He made it first debut on 14 August in a friendly-match against Armenia by coming as a substitute in place of Odise Roshi in the 56th minute.
His younger brother Klaus (born 14 December 1989) plays as a Defender for Stuttgarter Kickers in the 3. Liga.Basel