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.
