Siewert cast doubt on his future after their relegation was confirmed on the weekend.
But 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."