Sunday's loss to Crystal Palace saw the Terriers relegated to the Championship.
Hoyle said: "Jan Siewert came into the club at a difficult time and he would be the first to tell you that he's not happy with the results we've had so far.
"However, I believe Jan has made a big impact on the first-team already. He's made some big decisions and has shown a real understanding of putting the club first, before everyone else.
"I'm very pleased with the work he has put in and I'm genuinely excited to see what his team will look like after a full pre-season. The Board of Directors is fully behind Jan as the man to take us forward.
"Jan has a very clear playing identity, which is vitally important to us. It allows us to recruit players who will fit his style, which is where we had our success ahead of the 2016-17 season.
"As well as recruitment, we want to be the fittest team, the hardest-working team and show a real togetherness. If we put all those elements together, it'll be an exciting prospect for every Town fan.
"We know the Sky Bet Championship is a very difficult, competitive division, and I must stress that stability is the key next season. With Jan at the helm, a clear focus and our amazing supporters backing us all the way, there's plenty to look forward to. The future is still bright."