The 29-year-old has been on loan from the Midlands club this season but has now impressed Leeds manager Simon Grayson sufficiently to be offered a full-time contract at Elland Road.
It will be Pugh's second spell as a full Leeds player after he originally joined the Yorkshire side from English champions Manchester United in 2004.
Now, he will be aiming to help Leeds get promotion from the Championship after signing a two-and-a-half-year contract.
"Danny is a versatile player and is a good addition to the squad," Grayson told Leeds's website on Tuesday.
"He can play a few positions, he has already shown people what he is about, and it's good to have him on a permanent basis."
Pugh has made 17 appearances for Leeds this season as the former English champions look to return to the top-flight for the first time since 2004.