The pair took over in a caretaker capacity earlier this month, following the departure of Stuart McCall and Kenny Black.
While in the City dugout, Trueman and Sellars have so far claimed 10 points from a possible 12, recording victories over Cambridge United, Grimsby Town and Tranmere Rovers after a 1-1 draw at Crawley Town.
Trueman, 32, said: “We are very pleased that Ryan (Sparks - CEO) and the board have given us their full backing with this appointment, and the next steps.
“It takes the pressure off us as staff - with regards to no longer adopting a game-by-game approach - and gives us a clearer picture which allows us to focus on the club’s longer-term vision.
“We will continue to try and improve this group of players and, hopefully, keep the positive results coming.
“We know there will be ups and downs, but all we can do is prepare the team as much as possible to keep producing the level of performances and results they have been over the past two weeks.
“The January transfer window is just around the corner, and a great deal of work to further strengthen our squad has already taken place - and will continue to do so.
“The support both Conor and I have received from the supporters since taking charge has been deeply humbling. We are committed to ensuring the fans have plenty more to cheer about, over the coming months.”
Sellars, 28, added: “We are absolutely delighted to have been given the opportunity to continue leading the first team, and are very thankful to Ryan and the board for presenting it.
“We now look forward to putting a string of games together - to prepare for upcoming fixtures and get even more work into the players.
“Hopefully, the supporters can keep getting behind their team. We are looking forward to working to keep both the performances and results going.
“While we have enjoyed our start to life in a first-team environment, we have to be mindful that this will be a long season, and one which we are keen to tackle with everything we have.”
City’s chief executive officer, Ryan Sparks, said: “Mark and Conor have done a tremendous job in turning around our fortunes over the past two weeks.
“It is important they, our supporters and our partners have clarity, and we feel this provides it.
“Mark and Conor fully understand what we are trying to build and are excited about playing a big part in that.
“This is undoubtedly a huge opportunity for them. It is one we feel is dignified and respectful of what they have given us since the middle of December. They have improved our position, and we have taken steps to improve theirs - ensuring their futures are secure.
“Going into January, alongside our relatively-new recruitment department, Mark and Conor have our full support. They will have the final say on who comes and goes at the Utilita Energy Stadium, and have important resources at their disposal.
“I know the support they have had from our fans has meant a great deal to them. There is a huge sense of pride amongst us all at the moment, and I know they are looking to pick up where they left off, on Boxing Day, tomorrow evening.”