The 41-year-old singer - who has kids Teddy, two, and Charlton, eight months, with wife Ayda Field - has been granted permission to refurbish his London mansion, despite the Led Zeppelin rocker submitting a number of objections to his plans.
Robbie already withdrew two sets of plans after his famous neighbour claimed the work would damage his home, but has had his third application - which includes the removal of a swimming pool and gym, and construction of a new garage - approved.
However, planners at the Royal Borough of Kensington and Chelsea imposed conditions after consulting with Historic England.
A council report said: ''The vibration monitoring information states that there would be no harm to Tower House, which has an important interior decorative scheme and finishes as reflected in its listing at Grade I.
''Historic England has advised that the proposed works at the application site are modest and occur a reasonable distance away from the Tower House, and that there is no risk of the Tower House being affected by ground movement as a result of the proposed works.''
Williams will have to install equipment to monitor the level of vibration, which should not exceed 2.0 mm/s but tests at the site suggested this won't be an issue.
Any excavations must be dug by hand and hand tools must be used to break out existing concrete slabs.
The council also advised the 'Rock DJ' hitmaker to ask 71-year-old Jimmy - whose objections stated he worried the vibrations from any work would damage his property - if he can attach vibration monitoring equipment to his house.
Jimmy had also objected to the plans for a new garage, arguing the changes would be ''extremely unfortunate in architectural terms''.
Robbie and Ayda bought the house for £17.5 million in 2013.
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