Former Manchester United man Pugh joined the Yorkshire club in September on a short-term loan deal, with an option to make the switch permanent in January.
The 29-year-old has impressed in his 17 appearances so far this campaign, and has signed a two-and-a-half year deal at Elland Road.
Manager Simon Grayson told the club’s official website: “Danny is a versatile player and is a good addition to the squad.
“He can play in a few positions, he has already shown people what he is about, and it’s good to have him on a permanent basis.”
The deal marks a continuation of Pugh’s second spell with the club, whom he originally joined back in 2004 after failing to make his mark at Old Trafford.
The player spent two seasons at Elland Road before joining Preston North End for £250,000, and subsequently signed for Stoke when Tony Pulis’ men gained promotion to the Premier League.
Pugh becomes Leeds’ second addition in the current transfer window, after the club announced the signing of Tottenham youngster Andros Townsend, who joins on a loan deal until the end of the season.