Kiwomya has been caretaker manager of the 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."
Reflecting on his side's performance in Friday night's 4-1 victory over Bury, Kiwomya said: "I thought Zoko really made a difference second half. I thought first half we played too many square balls and got punished for it with the goal.
"Once we got the first goal the guys thought we can go on and win this. We asked a lot more questions and to do that you need willing runners and we had that second half, closing down their keeper and running 40 yards to close down a ball which we did well."
Kiwomya said his job at the moment was all about "steering the ship forward" and he was just relieved to get three points.
He added: "We needed a win to get a bit of confidence as we had lost a couple of games and put a couple of bad performances in.
"I said that we needed to get the win first before we could start thinking about closing the gap on the top six and this gives us the confidence to think we can break in to that top six."
Kiwomya's first game as manager will be against Tranmere at Prenton Park on Tuesday evening.