The ex-Beatles singer and songwriter - who was at the White House to collect the US Library of Congress's Gershwin Prize for Popular song earlier this year - decided to sit in on rehearsals before the White Stripes star performed 'Mother Nature's Son' for both him and the US president.
Paul, 68, explained: "There was a rehearsal first of all in the afternoon, and I came in and Jack's standing there, and I could see he was nervous, so I thought actually it would be good for them to have a rehearsal with me sat there.
"Get over the nerves, because it's going to be worse - he's going to be sitting there and Michele and the kids and then all the crowd. But I thought Jack's performance was great, very sensitive."
Paul played his track 'Got to Get You Into My Life' at the same concert, while Stevie Wonder gave his rendition of Paul's 'We Can Work it Out' and Elvis Costello played 'Penny Lane'.