The County Durham-born goal-getter was previously on the books of Middlesbrough and joins Blues on a one-year U19 professional contract.
The teenager is the son of former Stockport, Middlesbrough and Ipswich Town striker Alun Armstrong.
He will now link up with Alan Thompson's development squad, who got their competitive campaign underway with a 1-1 against Queens Park Rangers at Wast Hills earlier today
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On the arrival of Armstrong, Blues boss Lee Clark said: "We've had Luke in on trial over the last few weeks and we like what we've seen so far. He'll now primarily work with our development squad."