The pair and three other defendants sat at the back of the court for the 10-minute hearing.
The judge, Mr Justice Fulford, said they did not have to go into the dock.
He ordered that they all return to the court on March 8 for a plea and case management hearing.
Coulson and ex-News of the World royal correspondent Clive Goodman are charged with conspiracy to pay for information, including a royal phone directory known as the “Green Book”.
It contained contact details for the Royal Family and members of the royal household.
Coulson, 44, and Goodman, 55, face two counts of conspiracy to commit misconduct in a public office – one between August 31 2002 and January 31 2003, and the other between January 31 and June 3 2005.
The charges relate to the alleged request and authorisation of payments to public officials in exchange for information, including the royal contacts.
Brooks, 44, and former Sun chief reporter John Kay, 69, are charged with conspiring to pay Ministry of Defence employee Bettina Jordan-Barber around £100,000 for information.
The three each face one count of conspiracy to commit misconduct in a public office between January 1 2004 and January 31 this year.
That relates to allegations that Jordan-Barber, 39, was paid to provide information to the Sun.
All the defendants are on bail.