Dixon joined Cowell, David Walliams and Amanda Holden on the Britain's Got Talent panel earlier this year, reportedly collecting triple her £100,000 Strictly fee.
Speaking ahead of the BGT launch in Manchester, Cowell admitted to having an "unbelievable rivalry" with the BBC following Strictly's unprecedented ratings victories over The X Factor last year.
"With us and the BBC, I laugh about it, but there is unbelievable rivalry now," he said. "They want to be number one, I want to be number one. We do what it takes. It's a game - meant to be in good spirit, not supposed to be dirty tricks.
"But the Alesha thing was kind of fun. My decision to poach her was 70-30 on the fact she was on Strictly and the fact I liked her."
Cowell said he was hopeful that Dixon's signing would draw viewers away from BBC talent show The Voice, declaring: "[It] must have cost them at least £30 million, but I've got Alesha now."
The 52-year-old also came clean about his motivation to refresh the Britain's Got Talent panel, saying that outgoing judges Michael McIntyre and David Hasselhoff didn't do "a good enough job" last year.
"There are always stars waiting to be discovered," he argued. "Sometimes they need to be pointed in the right direction and I don't think that happened enough during the show last year.
"I genuinely like doing BGT. It was frustrating doing half and half last year - watching the auditions, not necessarily agreeing with all the decisions and then having to judge them in the finals. But I believe that I can find a star."
Cowell confessed today that he became "too cocky" about the popularity of his shows.