Asked if he knew about the 2009 decision, he told the BBC: "No, it was an administrative decision taken by the UK Border Agency."
The cards were then destroyed in 2010, when Theresa May was home secretary.
On Wednesday, Mr Corbyn accused the government of being "callous and incompetent" and asked if Mrs May, then home secretary, had "signed off" on the decision to destroy the landing cards which was now "causing such pain and such stress to a whole generation" of Windrush migrants.
She replied that the decision had been taken under the previous Labour government in 2009.
Mr Johnson suggested that Mr Corbyn had been "misled" over the issue: "The previous evening, as I understand it... Number 10 were briefing that this happened in 2010.
"What she had up her sleeve, whether it was deliberate or whatever - all's fair in love and Prime Minister's Questions - was that the decision was taken under us."
On BBC One's This Week, Mr Johnson - home secretary from June 2009 until May 2010 - said the UK Border Agency had taken the "administrative decision" to destroy the landing cards in 2009, although he was unaware of it.
"It wasn't just the Windrush landing cards it was this mass of paperwork that had built up over 50 years.
"And you have to remember, we were introducing a biometric identity card, compulsory, for anyone coming in from outside the European Union, so Windrush weren't involved in any of that, there was no threat to the Windrush generation.
"So it was an administrative decision, just at it was a year later, when Theresa May was home secretary - as my successor - and they were destroyed."
The Home Office has set up a task force to help people formalise their right to remain in the UK. But Home Secretary Amber Rudd has faced calls to quit over the scandal, with Labour saying she had blamed officials rather than taking responsibility for her department's actions.'
The Labour Party / BBC alliance had decided that the Windrush generation issue was going to be how they would destroy the electoral chances of the Conservative party in the upcoming local elections and hopefully take the scalp of Theresa May as well. The whole matter was pushed and promoted into the major issue of our times, leading to this week's PMQs when Jeremy Corbyn was to have put the blame firmly onto Theresa May and then for the whispering campaign calling her a racist and calling for her resignation would have got into gear.
Sadly for the BBC and the Labour Party the decision was taken under a Labour government. The line that made me laugh out loud in the above BBC article was this one:
'... Mr Johnson - home secretary from June 2009 until May 2010 - said the UK Border Agency had taken the "administrative decision" to destroy the landing cards in 2009, although he was unaware of it.'
If it had have been Theresa May who had been home secretary when the decision was made, would the BBC have accepted that it had been an "administrative decision"? Of course not, they along with the Labour Party would have been saying the buck should stop with her and calling for her resignation. But as it was a Labour politician, no action is required.