The 41-year-old becomes the ninth full-time boss appointed by Roland Duchatelet since he bought the club in early 2014.
Bowyer has no issue with not getting longer job security.
He said: “That [a deal until the end of the season] was my idea to put in. If I’m not successful I’m going to go anyway, that’s just football.
“The contract I was on, and I think Karl [Robinson, his predecessor] was on were six-month rolling ones. So if they wanted to get rid of you then they had to pay six months.
“There was no point messing about with that – just do it until the end of the season and leave me focusing on that. I know what I want us to achieve and if we don’t do it then that is my fault.”
Duchatelet is still seeking to sell the club and Bowyer was doing the role in a caretaker basis, which he first took on in March, until the end of the August transfer window.
“If new people come in and like what I am doing then I’m in a situation where I can negotiate for a longer contract,” said Bowyer.
“It all depends on myself. If I’m successful I will be here and if not then I don’t deserve to be.
“I’m in charge now but it’s just the same as before. Whether I was temporary, caretaker or manager – it’s one person making the decisions. That was me then and it’s me now.
“Nothing has changed with the players. I had their respect from day one and have still got their respect.
“It’s an honour for me to be working here – it is where I started as a player. Hopefully we can do what I believe my players are capable of, which is winning promotion. There is nothing more that I want than that.
“Everything is more settled now [that he has the job permanently]. Not so much for me, but for everybody else. Everyone else was more concerned, because they asked about it near enough every day. I knew one way or another it would get sorted out.”
Krystian Bielik is set for a scan on his injured calf after the Arsenal loanee missed Saturday’s 3-2 win over Wycombe.
Nicky Ajose and Darren Pratley both came off with hamstring problems.
“They need a little longer for the injuries to settle down before we can scan but they will be out for a minimum of two weeks,” said Bowyer.