The presenter, host of ITV1's Long Lost Family, announced that his dog initially alerted him to the problem by barking at around 5am. He went to investigate the disturbance.
"I went and had a look and I got up on the loo and looked out of the window, and there was a bloke in the garden trying to steal my bike," he told the BBC. "So I bashed on the window - I was stark naked. He looked up - he was a white guy mid 20s - and I raced downstairs and adrenaline completely took over.
"I would have gone into that garden and jumped on top of him stark naked. He would have needed trauma counselling for a long time. I ran into the garden and he just disappeared over the fence with the dog following me. I was so pumped up. It just took over me, I just wanted to get him."
Campbell, who won a Sony Radio Academy Award earlier this week, presented his Radio 5 Live breakfast show less than two hours later.
Police confirmed that officers were investigating an attempted theft. Campbell added on Twitter: "Just had excellent police and forensics round after my intruder incident."