Dan Evans is a prosecution witness at the trial of his former boss, Andy Coulson, and six others, on charges related to wrongdoing at the now-shuttered Rupert Murdoch-owned tabloid.
Evans told the trial that in 2005 he eavesdropped on Craig's voicemails and heard a message from a woman saying: "Hi, it's me. Cannot speak. I'm at the Groucho (Club) with Jude. I love you."
The call came from Miller's number. The newspaper later ran a story alleging an affair between the actress — then involved with Jude Law — and future 007 Craig.
Evans said Coulson heard the recording, then told him how to cover his tracks by making a copy, putting it in a bag and taking it to the newspaper's reception so it would look like it had been dropped off anonymously.
Evans has pleaded guilty to phone hacking at both the News of the World and the rival Sunday Mirror. On Monday he told the court he had accessed voicemails more than 1,000 times in all while at the News of the World between 2005 and 2010.
Murdoch shut the tabloid in 2011 after details emerged of the scale of its snooping on celebrities, politicians and others in the public eye.
Coulson, who edited the paper between 2003 and 2007, denies charges including phone hacking. The other six defendants also have pleaded not guilty.
Coulson served as communications director to Prime Minister David Cameron before resigning because of the scandal.