Delaney started playing youth football at Kjøbenhavns Boldklub (KB), the reserve team of multiple Danish champions F.C. Copenhagen (FCK). He made his debut for the Danish under-18 national team in October 2008, and played two matches for the team.
Delaney made his debut for F.C. Copenhagen, in an unofficial 2008 friendly in August 2008, after playing the first half of the 2008–09 season in the KB youth team, he was a part of the FCK squad in the Danish Cup 2008-09. Delaney made his official debut in the first leg of the semi-finals against Nordvest FC, where he substituted Hjalte Nørregaard in the middle of second half, in his time on pitch, he had a shot on the post.
In the return leg two weeks later Delaney was among the starting eleven. He played the first 60 minutes, before he was substituted with Şaban Özdoğan.
In the summer break 2009, Delaney was promoted to the first team squad together with Özdoğan.
He played the full-time in a match in Champions League qualification against FK Mogren. In this his international debut he even scored a goal. His first Superliga match was on 9 August 2009 against SønderjyskE, where he replaced Atiba Hutchinson in second half's stoppage time.
Determined on getting his breakthrough on the central midfield of the F.C. Copenhagen team, Delaney extended his contract with the club to 2015 on 6 July 2013. At the same time, he got jersey number 8. In the following season, Delaney has been regular starter on his favorite position, including UEFA Champions League matches against Juventus F.C., Real Madrid and Galatasaray.
On 23 January 2014, he further extended his contract to 2017. At the same time, he was officially named vice-captain of the team.
Delaney has played three games for the Danish U-18 national team, 11 games for the Danish U-19 national team.