The campaign has been launched by the Royal Parks Foundation of which Prince Charles is Royal Patron.
Nearly 40 years ago, The Royal Parks' gardeners planted 100 cherry trees along Chester Road. This February those trees were cut down, having reached the end of their natural lifespan.
The Royal Parks Foundation is now appealing to the public to make a gift or dedicate a new cherry tree in time for 100 new Prunus'Sunset Boulevard', worth £1776 each, to be planted this November.
Prince Charles said: "Historic avenues of trees are one of the things that make the Parks so special, which is why I am so pleased to support the Royal Parks Foundation's vision to restore the Cherry Tree Avenue in The Regent's Park.
"The proposed planting will bring pink tinted blossom in the spring and yellow-golden leaves to lift the spirits every autumn. I am sure the many visitors to the park will derive great pleasure from this changing spectacle of the seasons."
Supporters have already dedicated more than 50 trees and raised £100,000, which will go towards maintaining both the avenue and Queen Mary's Gardens.
The tradition of planting cherry trees in Regent's Park began in the 1930s, when Queen Mary's Rose Garden was created with donations from the artist Sigismund Goetze. The last cherry tree (Prunus 'Kanzan') was planted on Chester Road in 1978, and was removed in February of this year.
Wood from the old trees will be recycled into bird boxes and other artefacts to go back into London's green spaces.