Roscrow, 25, has penned a lengthy three-and-a-half year deal at Park Hall after making the switch from the League One outfit for an undisclosed fee, making the striker the club's new record signing.
The Saints believe the swoop for Roscrow, who netted 21 goals in the Cymru Premier helping Cardiff Met University secure Europa League football two seasons ago, is a signal of intent to potential investors in Welsh football.
Chairman Mike Harris has promised more statements of intent from the 'prudent' Oswestry outfit.
The striker made just six substitute appearances for the Dons in League One this season, but scored twice in four EFL Trophy appearances.
"This will be the first, but not the last significant signing either," Harris said. "We’ve been prudent as a club, and as we take advantage of the current financial climate, we want to continue to build, not just for The New Saints but also Welsh football as a whole.
"We have come so far in the last twenty years but there’s still a long way to go.
“Adam Roscrow’s signing also sends out a signal to potential investors. Why not invest in Welsh football? You get more for your money and there’s a greater chance of European football."
Roscrow, who has scored once in two Wales C internationals, adds considerably more firepower to boss Scott Ruscoe's ranks as TNS go about re-claiming their top flight crown after Connah's Quay won the title last term.
The Saints lead the way by three points to Connah's Quay in the top flight, albeit having played once more than their rivals.
There has been no action since December 19, after which Cymru Premier action was paused indefinitely as its elite football status was rescinded after the number of positive Covid-19 cases in Wales. There will be no matches in Wales until January 16 at the earliest.
Ruscoe said of his latest capture: “We are very happy with the signing of Adam Roscrow, which further strengthens our attacking options. A goalscorer who knows the league well, who’s hungry to progress and is a very good team player as well.”