Capello spoke to AC Milan vice-president Adriano Galliani about the move.
Becks will join AC Milan on loan in January.
A top Milan source told The Sun: “It was Capello’s endorsement that convinced Milan to sign Beckham.
“He told Milan vice-president Adriano Galliani ‘Beckham is a very good player and if you sign him you will see how good he still is’.
“That’s all the club needed to hear. From then on Milan focused on turning Beckham’s stay into a loan.”