Johnson has been at the helm since 2009 but will leave to pursue new opportunities.
Duggan will take on the role from June 30 but he will remain on the board of Broker Network.
Lindsay Forster, group marketing director, is also leaving the group for Friends Life.
Her successor is Claire Chambers, who joins from Aviva.
Mark Hodges, chief executive officer of Towergate Insurance, said: “Tim has made a significant contribution to Towergate, notably the creation of the CCV Business and his leadership of Paymentshield over the last five years.
“Tim will remain a strong supporter and a shareholder of Towergate. I would like to thank Tim and Lindsay for their contributions to the Group.”
Following Duggan’s departure Broker Network is now looking for a new chief executive officer.