The Sulphurites held out until the last minute to keep hold of their top-scorer for the last two seasons, but Wrexham came in late in the window to do the deal.
As late as Wednesday night, manager Simon Weaver said Armstrong would be saying because no club looked likely to come up with the money that would allow them to sign a replacement.
Armstrong had refused to play om the first two games of the season pm in an attempt to push through a move.
But Hollywood-owned Wrexham did eventually come up with the money, allowing Harrogate to bring former loanee Josh March back to the club from Stevenage.
Both deals were only announced after the 11pm deadline and the Football League have confirmed Wrexham did not submit the paperwork in time.
Now the Wetherby Road club will have both for the rest of the year.