After losing his first game in charge, the Magpies have now gone three games unbeaten in League One.
Chairman Ray Trew told the club's official website that Kiwomya "deserves" the chance to lead the team until the end of the current campaign.
"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," he said.
"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."
Notts County are ninth in the table.