The 23-year-old will join from English Premier League side Everton for the remainder of the campaign.
However, it looks like their bid to bring in Tottenham Hotspur midfielder Japhet Tanganga has fallen through with Spurs boss Jose Mourinho keen for the player to remain London, according to Sky Sports.
The reigning Scottish champions wish to add to their squad ahead of the transfer window closing later this evening as they look to end a dismal 2020/21 campaign on a high.
Kenny arrives as a direct replacement for former right-back Jeremie Frimpong. The Dutchman left for Bayer Leverkusen earlier this month in a deal reported to be worth in the region £12 million.
Manager Neil Lennon said of Kenny’s arrival: "We just need the paperwork to be finished. He has been in the building, he travelled up last night so hopefully we can get that signed and sealed this afternoon."
“He's a player I have liked for a while. He is at Everton obviously and had a very good career at England youth at under-21 level and I watched quite a bit of him last season when he was on loan at Schalke.
"I like his qualities, his enthusiasm for the game, his character and I think he will bring that to the team. He is a bubbly sort of personality and he plays that way as well. He is ready to start and itching to play as well."
The Celtic boss was not so pleased about the late development in the club’s pursuit of Preston North End defender Ben Davies.
The Hoops looked set to agree a pre-contract deal with the 25-year-old, only to watch as Liverpool swooped in at the eleventh hour and had an immediate offer accepted by the Championship side.
Lennon said: "It's a blow because we were very close to doing that and obviously we got gazumped at the last minute by Liverpool.
"He lives in that area and I'm sure financially it would have been quite rewarding for him as well. We’re disappointed but we move on."