The former Manchester United captain made the revelations in his explosive new book, The Second Half, as he laid out details of his six-month stay at Parkhead.
Despite rival offers from Real Madrid and Everton, Keane opted to sign for Celtic - but only did so to spite him.
“Real Madrid offered me a year and a half. Emilio Butragueno made the call and said ‘Roy, we’ll be glad to have you’.
“I met David Moyes at his house and was impressed with what he wanted for Everton. When a club is interested the manager generally sells it to you.
“I met Gordon Strachan in London at Dermot Desmond’s house. Gordon told me ‘I’m not really worried if you sign for us or not. We’re OK without you’. So I said to myself ‘f*ck him, I’m signing.”
“I think it was one of the reasons I signed for Celtic - to prove Gordon wrong.
“He was letting me know he wasn’t desperate for me; he was being a bit coy. But there was a bit of defiance from me.
Keane also revealed how he considered quitting Celtic after his first training session because of intense pain in his hip, and had initially cursed himself for not retiring after leaving Manchester United.
“I lay there thinking: ‘I don’t want to go back. But I need to. I have to. You should have retired. You should have just packed it in.’
“But I couldn’t leave after my first day. Imagine how that would have looked.”
Keane also said the Old Firm derby was his favourite experience during his stay in Scotland, and said he enjoyed the “hatred” of the atmosphere.
Describing the atmosphere of a 1-0 win over Rangers at Ibrox, he said: “The atmosphere was brilliant, f*cking electric. The hatred, I enjoyed all of that.
“The dressing room afterwards was great. I met great people at Celtic from John Clark to the late Tommy Burns. I’ve no regrets about signing. It’s a brilliant club.
“When I phoned Gordon at the end of the season to tell him I was going to have to call it a day because of my hip Gordon went ‘All right, it’s for the best’.
And I was saying to myself ‘Try and persuade me, for f*ck’s sake. At least pretend.’”