Coventry City this week completed a deal for the Northampton goalkeeper, offering Dunn the chance of Championship football next season although he will have to battle Joe Murphy for the number one jersey at the Ricoh Arena.
Johnson, who has made Arron Davies the latest addition to his squad, will now search for Dunn's replacement as he puts the finishing touches to a side expected to challenge for promotion despite coming off the back of a dismal League Two season.
He said: “We have various options as we look for a new goalkeeper and I am confident we will be able to bring in a good replacement for Chris.”
Dunn departs having made over 100 appearances in all competitions for the Cobblers.