Westminster Council will write to those living in the area's most expensive properties to make an extra voluntary contribution on top of their council tax to help pay for local projects.
The scheme is expected to be given the green light after a consultation in which more than 400 people said they would support the initiative.
Council tax rates, which are among the lowest in the country, have been frozen.
But letters will be sent to homeowners in the highest council tax bracket - Band H - asking them to pay an extra £833.
The money raised is earmarked for projects aimed at helping young people, rough-sleepers and the lonely.
Council leader Nickie Aiken said the scheme was developed after wealthy residents said they wanted to pay more.
"The outcome of our consultation reflects the kind and generous spirit of Westminster residents," she said.
"It also confirmed what I had heard from people I had met on the doorstep that those in the more expensive homes are willing to contribute more to community projects.
"The scheme is most popular among residents of the most expensive homes."
The Archbishop of York, Dr John Sentamu, congratulated the council on its "imaginative initiative".
"May all of us who are willing to do this be given the facility to do so," he said. "Thank you, Thank you! - You are fantabulous!"
Some of the borough's well-known residents have also voiced their support.
DJ Tim Westwood said: "Asking people who have done well to contribute a little extra seems a very good idea to me.
"I also like the fact that young people will be among those who benefit from any money raised."
Margaret Mountford, who appears in BBC reality TV show The Apprentice, added: "In principle this is a very good idea, but obviously we need to see the detail.
"There are clearly areas of need in the borough where money raised could be spent."