Ioannou joined Manchester United youth academy at the age of 11. He played at the Marveld Tournament with the under-15 team in June 2010 held at Netherlands. This was followed by his participation in Manchester United Premier Cup. His form earned him a two-year scholarship in June 2012. He made his debut in Old Trafford against Charlton Athletic in FA Youth Cup aged 16. In his last match for the reserves, he captained his team against Tottenham Hotspur. He also appeared in three 2013–14 UEFA Youth League group stage matches with Manchester United U19 team.
After being released by Manchester United, he signed a three-year contract with APOEL in April 2014. On joining the club, Ioannou commented: "My main aim is to win trophies of course, but obviously I need to start playing. APOEL play in big competitions – Champions League and Europa League – so hopefully I can get a few games.”
He made his official debut against Finnish club HJK Helsinki on 30 July 2014, in APOEL's 2–2 away draw for the third qualifying round of the UEFA Champions League. On 5 November 2014, aged 18, he made his first UEFA Champions League group stage appearance, playing the full 90 minutes in APOEL's 0–1 defeat against Paris Saint-Germain at Parc des Princes. In his first season at APOEL, Ioannou appeared only in seven matches in all competitions, but he managed to win the double, as his team won both the Cypriot championship and the cup.
On 3 June 2016, Ioannou signed a three-year contract extension until 31 May 2019, but a few months later, on 13 March 2017, he signed a further two-year contract extension with APOEL, running until 31 May 2021. Following his successful 2016–17 season with APOEL, Ioannou awarded the "Young Player of the season" award by Cyprus Football Association.