The full-back has fallen out of favour at White Hart Lane, having made just five Premier League starts under Mauricio Pochettino this season.
A move to Swansea has been widely reported in the British media over the past couple of days, and in a press conference on Thursday Monk revealed that Naughton was at the club and putting the final touches on the deal.
"He's here. It's the last bits of the contract to sort out, the legal side," he said.
"He trained with us this morning and it's good to get it done.
"He brings a good pedigree, is experienced at this level, a good age, we look for players looking to prove a point and who are hungry.
"He enjoyed his time at Tottenham but perhaps didn't get the game time he wanted. Now he'll be looking to push on.
"It's testament to how far we've come that players look at us. Kyle's a great person and a good player the type we need at the club.
"I played against Kyle, so I know what he can do.
"I looked at him in the summer and kept an eye on how he's progressed over his career but have had a close look since becoming manager and when the opportunity came up we took it.
"We're still on the lookout to add to the quality we’ve got."
Monk also confirmed that Swansea had received a bid for left-back Neil Taylor, with Crystal Palace widely reported to be interested, but the manager said: "It's not my concern, it's down to the club, but he's happy here and I'm happy with him."
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