The 'Late Late Show' host has recalled how he was invited to present at an awards ceremony where the 56-year-old actor was being honoured and afterwards, the Hollywood star - who plays Ethan Hunt in the spy movie franchise - went to a ''ridiculous amount of effort'' to get his digits to Corden so he could ''stay in touch'' with him.
The comedian told Howard Stern on his SiriusXM show: ''His publicist got in touch and said he was being honoured with a big filmmaker's award in Vegas.
''And would I go and host it as a surprise. I said, 'Absolutely!'''
The 'Top Gun' star told Corden: ''Stay in touch, give me a call'', to which he replied: 'Tom, that's really lovely, but I don't have your phone number.'''
And Cruise responded: 'I'll get it to you.'''
A couple of days later, the 'Gavin and Stacey' star arrived into his office in Los Angeles and was greeted by balloons and a surprise package to say thank you.
When he opened up the box, Cruise had gotten a phone cake made with ''odd symbols'' representing his number for the British funnyman to solve and a letter with the famous, ''Your mission, should you choose to accept it'', line from the blockbuster movies.
He recalled: ''In conference room one was a massive amount of balloons that said 'thank you' and a box.
''I opened the box and there was a cake in the shape of a telephone with all these odd symbols on the dial. Then in an envelope was a dictaphone and it said 'press play'.
''It says, 'Your mission, should you choose to accept it, is to work out the code and call the number on your cell phone. This message will self-destruct in five seconds'.''
Corden managed to get the number after several attempts and Tom answered the phone and the pair have been close friends ever since.
He said: ''I called and this voice went, 'Hello?' I went, 'Is that Tom Cruise?' And he went, 'Is that James Corden?' I said, 'Yeah', and he went, 'Well now you've got my number!'
''It's just the most amazing thing.''
His new album Underneath It All is out now.
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