Born in Kumasi, Ghana, Adu started his professional career in 2006 at local club Liberty Professionals F.C. On 23 September 2008, he moved from Liberty Professionals to French Ligue 1 club OGC Nice and signed a contract extending to 2011. He completed the move with national teammate Abeiku Quansah. On 26 March 2010, Adu went for a trial at Swedish club GAIS. Adu later signed a contract with Danish Superliga club FC Nordsjælland on 16 July 2010.
FC Nordsjælland
Adu quickly became an important player for FC Nordsjælland as he took a permanent position in the starting eleven. He played continuously in the league, cup and European competitions at his first season at the club. Adu was part of the Nordsjælland squad that won the Danish Cup during the 2010–11 season, also participating in the final of the competition. Adu continued to be an important player for the club as they won their first league title in the 2011–12 season. Subsequently, the club qualified for the 2012–13 UEFA Champions League where Adu participated in all six group stage matches when Nordsjælland finished last in their group. Halfway through the 2012–13 season Adu transferred from Nordsjælland to Belgian Pro League club Club Brugge.
Club Brugge
After transferring to Belgium Adu played fairly regularly during the remainder of the 2012–13 season. However, during his second season at the club he played less regularly and was loaned to Norwegian newly promoted Tippeligaen club Stabæk until the summer of2014.
On 8 July 2014 reigning Swedish champions Malmö FF announced that they had signed Adu from Club Brugge as reinforcement for the clubs campaign to qualify for the 2014–15 UEFA Champions League. The transfer was originally meant to be carried out on 1 August when Adu's loan contract with Stabæk ran out, however Malmö FF has confirmed that they were in negotiations with Stabæk to acquire Adu when the Swedish transfer window opened on 15 July. At the same time it was also confirmed that Adu would wear the number 8 shirt at the club. On 24 July Stabæk announced that they had agreed to terminate the loan deal prematurely for a minor compensation from Malmö FF. Adu made 15 appearances for Malmö FF during the latter part of the 2014 season, helping the club defend their league title and qualify for the group stage of the 2014–15 UEFA Champions League. Adu was a regular in the next Champions League campaign in 2015–16 as Malmö FF once again qualified for the group stage.
