Kiwomya has been caretaker manager of the npower League One club for four matches since Keith Curle was sacked at the beginning of February following a 2-1 defeat at then-bottom club Hartlepool.
After losing his first game away at Stevenage, Kiwomya is unbeaten in three outings. The former Arsenal and Ipswich striker gained his first win on Friday night as the Magpies came from behind to beat Bury 4-1 at Meadow Lane.
The result lifted them up to ninth in the table and eight points adrift of the play-off places ahead of Saturday's games.
The Notts County board have been impressed with Kiwomya's work and have put their faith in him for the club's remaining 13 matches.
Chairman Ray Trew said via a statement on the club's official website: "Chris has shown his desire and enthusiasm for the job and coupled this with a tactical astuteness that has allowed him to turn things around when they haven't been going exactly as we would have liked.
"We think Chris deserves the chance to build on the work that he has done in the short space of time that he has been in charge of first-team affairs and we are happy to confirm that he will be at the helm until the end of the current campaign.
"We will, of course, review the situation at the end of the season, but Chris now has the chance to show us exactly what he can do, in the knowledge that he has an extended spell in charge."
Kiwomya's first game as manager will be against Tranmere at Prenton Park on Tuesday evening.