In January 2015 Dundee United turned down two transfer offers from Celtic for Armstrong, however the transfer was completed on 2 February 2015, alongside fellow Dundee United player Gary Mackay-Steven. Armstrong denied requesting the transfer. Both players would be ineligible for the remaining Scottish Cup and Scottish League Cup ties of the 2014-15 season as Celtic chased a domestic treble. Armstrong and Mackay-Steven were later given the nickname Zig and Zag by the staff at Celtic.
Armstrong scored on his Celtic debut in a 3-0 league victory at Partick Thistle on 11 February 2015. He gave Celtic a 2-0 lead after fellow debutante Gary Mackay-Steven opened the scoring. Armstrong made his Celtic Park and European debut in a 3-3 draw with Inter Milan in the UEFA Europa League on 19 February 2015.
Armstrong made his first appearance of the 2015–16 season, in the UEFA Champions League second qualifying round first leg tie against Stjarnan, assisting the second goal in a 2–0 home win. He scored his first goals of the season with a second-half brace, in a 4–2 league win against Inverness CT on August 15. He claimed assists in back-to-back matches in January, in wins against Dundee United and Hamilton, the latter result was an 8–1 home victory, the biggest recorded league win since the formation of the Scottish Premiership in 2013. His next goal came in a 3–1 league defeat of St Johnstone four days later.