In 2008 Birkir had a successful loan spell at newly promoted Tippeligaen side Bodø/Glimt,[4] playing a big part in them finishing fourth in the league.

On 12 January 2012, it was announced that Birkir would sign for Belgian Pro League side Standard Liège on a five-year deal.

After the end of the 2011–12 season, in July 2012, Birkir joined the newly promoted Serie A side Pescara on a season-long loan deal, for €300,000, with an option to sign for an additional €900,000.

[8] Pescara bought Birkir from Standard Liège on 9 June 2013 on a permanent transfer for a previously agreed fee,[7][9] with the aim of selling him for a higher amount that summer with interest being reported from clubs in the top leagues in England including, Italy and Germany.

On 20 June 2014, it was announced that Birkir would sign again for Pescara on 1 July 2014, after the club won the co-ownership bidding for the player from Sampdoria.

They beat Vicenza Calcio 3–2 over two legs in the semi-finals, with Birkir scoring the crucial match winning aggregate goal for Pescara on 2 June 2015 to help them qualify for the Serie B playoff final against Bologna.

[17] On 7 July 2015, it was announced that Bjarnason had signed a contract with Swiss Super League club FC Basel for €1 million.

EFL Championship team Aston Villa, following their relegation in the preceding Premier League season, showed interest and on 25 January 2017 Basel announced that the club had signed the player.

[26] On 18 January 2020, Birkir returned to Italy, after signing a 1.5-year contract with Serie A side Brescia,[27] after a short spell in Qatar playing for Al-Arabi.

Birkir's goals and performances played a crucial role in the qualifiers helping guide Iceland to the World Cup playoffs, however in November 2013 they lost 2–0 on aggregate over two legs to Croatia.

[33] He was called up to the national team again for UEFA Euro 2016 and achieved the honor of getting his country's first ever goal in a major tournament when he scored the equalizer against Portugal in their first group match.