The 24-year-old striker has penned a two-year deal with the Bucks after leaving Harrogate Town last week.
A striker, Williams previously played for Brackley Town two seasons ago, netting 33 goals on their way to FA Trophy glory.
His arrival at New Bucks Head is sure to soften to blow of losing top-scorer Daniel Udoh to Shrewsbury Town.
"Signing Aaron shows how far we have come in such a short space of time," Cowan told the club's website when speaking about the ex-England C man.
"Lots of clubs were in pursuit of his services but after numerous meetings between myself, Aaron and his family, he decided AFC Telford United is the place for him.
He's another piece of the jigsaw," Cowan added. "I am sure everyone within our club will welcome him with open arms."