The 47-year-old was originally due to sign a new deal in November but a scheduled press conference was cancelled in the wake of the FA Cup replay defeat to Kettering.
"The situation perhaps carried on longer for everybody else than it has for us because it was a situation we were all comfortable with," Wright told the Lincolnshire Echo.
"In respect of the delay, I certainly don't think it has done any damage at all, but we are getting to the latter stages of re-negotiating with players over their contracts for next season and it's important that they're clear as to who'll be in charge.
"It has been sorted out, finally, and I'm delighted to have Peter on board because he is a very good manager. If you want success, then you need stability."