Duckworth arrived from non-league outfit Bradford Park Avenue on a short-term deal at the end of August after impressing boss Colin Cooper during a pre-season trial.
And the 21-year-old has gone on to make six appearances and earned himself a longer deal.
"I've been very impressed with Michael," Cooper told the club's official website.
"The way he's come in and gone straight in to the team, I think everyone at the football club was keen to tie him down on a full, professional contract for a longer period."
Duckworth added: "Getting a first proper professional contract is brilliant and I'm just so happy to get everything sorted out.
"I think I've fitted in nicely with the group; the lads have been great with me and the gaffer is obviously happy with what he's seen so that's the main thing."