The council also said it has implemented a range of measures to help residents affected by the tragedy, including the extension of a rent-free period for families until July 2019.
Council tax, service charges and utility charges will also be written off for this period.
Adult residents who lived in the tower or nearby Grenfell Walk and moved out of emergency accommodation will be offered a £300 a week allowance for the first three months, and each child will receive £150 a week. Weekly support for a second three-month period will be paid at the rate of £150 per adult and £75 per child.
The council is also spending £235m on 300 new properties to give residents more accommodation choices. It said it believed this was the biggest local authority house-purchasing programme in recent history.
The interim report from the Grenfell Tower taskforce was published on Monday and was scathing about RBKC's response to the fire, describing it as "sluggish and chaotic".
Communities secretary Sajid Javid also highlighted an impersonal approach to dealing with people who approached the council for help.
Kim Taylor Smith, deputy leader of RBKC, acknowledged that the council "still [has] a huge amount to do", but he said "the green shoots of recovery are growing."
“We understand the need to change the council, the way it works, the way it listens, and the way it acts. That new leadership is in place, we have a dedicated team working around the clock to meet survivors’ needs and are announcing today an unprecedented rehousing support package to help those affected by this devastating fire," Taylor Smith said.
“We want to help get everyone that wants to move into a new home the opportunity to do so by Christmas.”
Councillors are hopeful that all affected Grenfell survivors will be moved into new homes, with furnishing and moving costs covered, by June next year.
