Kiwomya, who had been in temporary charge of the Magpies since the departure of Keith Curle last month, first joined County as development squad manager in February 2012, having previously been the reserve-team coach at Ipswich.
Chairman Ray Trew told the club website: "Chris has showed in the short time that he has been in charge of the first team that he has a great passion for the game, is tireless in his endeavours, communicates extremely well with the board, sharing our vision, and anyone who has been fortunate enough to speak to him in person will have seen his enthusiasm for every detail of every performance.
"When making this appointment we were looking for someone who could realise our long-term vision for the club, someone that we could work with to bring progressive success alongside the development of young, homegrown talent from our successful youth set-up.
"Chris is well respected throughout the football community for his ability to develop players, as well as spotting raw talent in youngsters, something that we are confident will help foster stronger working relationships with clubs, particularly at a higher level.
"We are not putting any immediate demands or expectations on Chris, we have said to him that the team is his to mould as he sees fit and to prepare for the new season.
"That may mean a change of personnel over the summer, but everything will be done with a view towards building for the future. We are not demanding instant results, we see this as the start of a project, one that we are asking our supporters to get behind as we look to grow together as a club."
The Magpies, who are seven points adrift of the play-offs with nine games to play, have lost two of 11 matches under Kiwomya's stewardship.