Armstrong, who – like Eames – has a background in sports science, has worked at a number of leading EFL clubs over the last 20 years.
He served on the coaching staff under Dave Jones at Southampton, Wolves, Cardiff and Sheffield Wednesday before working with Bahrain’s national team.
Since then Armstrong has had a two-year stint as assistant coach with New Zealand.
Eames said: “Alex has got a fantastic background. One, he’s a coach, but he also has a sports science background and he’s worked at some fantastic clubs like Wolves and Cardiff.
“One thing that strikes me about Alex is he’s a winner – he’s got promotions under his belt as an assistant manager, he’s been to an FA Cup final and he’s going to add a huge amount at Barnet.
“Alex will be pivotal to our success going forward, bringing his experience to all staff. We’ll leave no stone unturned and I’m really looking forward to him starting here.”