Welshman Davies, 24, has been a big hit on trial with his new Bucks team-mates throughout pre-season and moves to the New Bucks Head after a prolific stint in Welsh football.
Davies has been lethal for previous club Prestatyn Town, firing more than 70 goals in two seasons to help them to the Huws Gray Alliance League title – the second tier – before Prestatyn were relegated after one season in the top flight.
The striker's goals had reportedly interested several other suitors but Davies has been rewarded for impressing on trial.
Cowan has tipped the hard-working Wrexham-born frontman to be a firm favourite with the Bucks faithful.
The Telford chief said: “Jordan has worked extremely hard during pre-season and I am sure our supporters will love his style of 'never give up' play.
"He’s scored a lot of goals at the level he was previously playing so now he gets his chance to prove himself here.
"He’s fitted in great and we look forward to seeing him score goals at our club."
Davies, who has previously played for Market Drayton, was on target for Telford in their first friendly victory against Ellesmere Rangers.
He joins fellow trialist Dominic McHale in penning terms at the New Bucks Head for the coming National League North campaign, which begins in two weeks with Telford at home to Brackley Town.
Davies said: "I am delighted to have signed for AFC Telford United, I would like to thank the gaffer and his staff for giving me an opportunity to play at this level I can’t wait to get going now."
Cowan's side head to Wrexham on Wednesday for a second contest against the Red Dragons.
They had been due to close their pre-season schedule at home to Macclesfield Town on Saturday but that fixture is in doubt after the National League side were wound up in court.