Terriers chief exec Jake Edwards said: "I'd like to express our huge gratitude for everything they've accomplished over the past 7 months. Few management duos could have kept us in the Championship and they've solidified their legendary status. There is much love for them and they are welcome back here with open arms.
"Kevin and I were delighted when they agreed to stay on. All parties were clear it would not be a long-term appointment but would help us to establish the new regime at the club.
"We feel we are ready to move forward with our long-term plans to drive the club back into the Premier League and to make a longer-term managerial appointment. We have discussed that and the timing of it with Neil, and after spending time with his coaching staff he has graciously agreed now is the time for that to happen."