[5] In 2011, his side reached the final in the Norwegian Cup, where Birkir played the whole game as Brann lost 1–2 to Aalesunds FK.

[7] During the reign of Swedish manager Rikard Norling, Birkir however lost his place as a regular starter at Brann.

[8] The relegation also put an end to Birkir's 6.5-year spell at Brann, who transferred to the Swedish top-tier club Hammarby IF in December 2014.

[10] At Hammarby he began the 2015 season as a centre-back, but eventually moved back to his natural position on the right flank after the arrival of Richard Magyar.

[13] At the end of the year, Birkir sought to leave Hammarby at the expiration of his contract, seeking a new club ahead of the 2018 FIFA World Cup.

[22] Birkir was praised for keeping the Portuguese winger Cristiano Ronaldo at bay in a group stage draw,[23] as well as neutralizing Raheem Sterling in Iceland's sensational 2–1 win against England in the round of 16.

On 15 April 2019, it was announced that Birkir was appointed as an assistant coach to 3. deild karla club Knattspyrnufélagið Hlíðarendi.