Miazek, 21, has been on the hunt for a club since leaving Chojniczanka Chojnice last summer.
INNfootball Agency posted a snap on Twitter of the former Poland Under-19 international putting pen to paper on a deal with Leeds.
They captioned the image: “Done deal. Officially confirmed – Kamil Miazek a @LUFC player.”
Miazek has been pitched straight into the action, starting for Leeds’ Under-23s against Hull City at Thorp Arch this afternoon.
He conceded in the 39th minute with Hull’s fit-again striker Will Keane netting.
Miazek arrived for a trial with Leeds at the end of September after a training spell with Championship rivals Barnsley.
It was revealed in October by Elland Road academy scout Jakub Bokiej that the club had made an approach for his signature.
“Kamil Miazek has received an offer of the contract from Leeds United,” Bokiej tweeted.
Miazek, who also played for Feyenoord, has one cap for Poland’s Under-19s to his name.