The decision looked likely after no objections were lodged against the proposal during an eight-week planning process.
The U2 singer, aka Paul Hewson, and his wife Ali applied for the 53sqm "plant room" on May 7. The room at Temple Hill on Vico Road will be used to house energy efficient boiler technology.
And the multimillionaire rock star will even be able to avail of a €2,500 Government grant, now that he has been given permission for the plan.
Sustainable Energy Ireland, the country's energy agency, said grants for wood pellet boilers are not means tested. A letter from architect Colin Jennings accompanying the application stated: "The proposed use of the structure is to house a new wood pellet boiler for the main house with associated pellet storage and services." Mr Jennings stated the equipment could not be accommodated "within the existing house and any of the existing structures on site would not be suitable".
He said the plant room "will be fully concealed underground and will be situated below the front forecourt of the existing main house".
The structure will be "accessed externally from the lower ground floor light well". Mr Jennings added: "The structure is placed away from the building in order not to interfere with any of the existing front walls of the house."
Bono's latest plans for his seaside home are far more low-key than previous proposals.
The singer has lodged several planning applications with Dun Laoghaire council in the past, most recently getting permission for a massive redesign of the property.
Bono and Ali were given permission in November to add a new floor to their home. Bono is currently on a world tour with the band, promoting their new album No Line on the Horizon. The 360 tour kicked off at the Camp Nou in Barcelona.