The jury at the phone hacking trial heard how the editor became "very animated" after hearing a recording of the voicemail in which the actress - who was in a relationship with Jude Law, the actor, at the time - could be heard telling the James Bond star, "I love you".
Dan Evans, a former News of the World and Sunday Mirror reporter, who has admitted phone hacking for both papers, said he intercepted the intimate message in 2005, after being told to "jump off a cliff" if he did not come up with a front-page story. After Coulson was played a recording of the message, Mr Evans said the editor ordered him to make a copy and send it to the front gate of the newspaper's headquarters in Wapping, east London, in order to make it appear as if the recording had been delivered anonymously.
Giving evidence for a second day, Evans, 38, explained that he had been "monstered" by a senior colleague and told his job was on the line if he did not come up with an exclusive.
Evans said: "That weekend I did everything I could to make sure I came back with a front-page story. I hacked every phone I could possibly think of hacking, that included one of an actor called Daniel Craig."
He added: "On that voicemail, I heard a female voice saying, 'Hi, it's me. I can't speak. I am at the Groucho with Jude, I love you'." Evans said when he checked the number of the person who had left the message, it matched that of Miller, who was a regular fixture in tabloid newspapers at the time. He said he had gone to work after the weekend with his "tail wagging" and had played a recording of the message to Coulson and other journalists at the paper.
He told jurors: "Andy became very animated, [saying] 'brilliant'." Another senior colleague had told him: "You're a company man now, Dan".
Evans said after listening to the voicemail recording, Mr Coulson ordered that a copy be made and the original destroyed. He went on: "Andy wanted to preserve the tape but not in its original recording so he said to me, 'You need to make a copy of the tape. Put it in a Jiffy bag and have it sent down to the front gate and get them to say it has been dropped in anonymously'.
The idea was that if push came to shove we would say that someone had sent it in and that's what sparked it all off."
On Monday, the Old Bailey heard how one of Law's relatives had also sold information to the newspaper about the relationship, but the intercepted voicemail helped to confirm the story.
Mr Evans explained that after the editor heard the tape, he was sent to Craig's north London home.
He said that after Craig answered the door, he told him: "I am Dan Evans from the News of the World. I am very sorry to do this to you, but we are running a story saying you are having an affair with Sienna Miller. Have you got anything to say to that?
"He said, 'No, no, no, it's not true' and shut the door."
The story did not appear that weekend, but was published the following Sunday.
Evans told the court he would like to apologise to all of the people whose privacy he had infringed.
Coulson denies a charge of conspiring to intercept communications.
The trial continues.