He told BBC Radio Lancashire: "It's going to be a big change in my life and I'm going to have to deal with it, it's the right time to take stock."
He continued: "I've known for quite a while and I now know the path that we have to take, obviously it's going to take up time so I just couldn't carry on."
Kilby, who will remain on the board as a director, said he had agonised over the decision to step down: "It's been a long time, 13 years and a big part of my life, so it wasn't taken easily but circumstances have made it for me.
"We have a very tight board, there are five of us and it's up to the board of directors to elect its chairman.
"No doubt we'll all be having discussions, and at the board meeting at the end of May, we'll elect a new chairman then," he concluded.
Football manager Eddie Howe has told his boss that the team will give everything they’ve got to finish his last season as chairman on a high.
And Howe believes marking the end of his reign with a repeat would be a fitting send-off.
“I can think of no better way,” he told the local media on hearing the news.
“We'll work as hard as we can day to day to make that happen. Who knows what's round the corner, but we would certainly love that ourselves.”
“When you get news like that it might have a uniting effect, for sure. I think it was a surprise to a lot of people.
“It’s incredibly sad.''