The BBC has commissioned an initial run of 20 ten-minute monologues from Sir David, reports The Times.
His Radio 4 monologues, which will cover the history of nature, will be broadcast on Friday night.
Cooke's landmark series ran for 58 years until 2004, when the presenter died at the age of 95.
Radio 4 controller Mark Damazer said Sir David's The History Of Life would be similarly "intimate and authoritative".
"Sir David will continue the Radio 4 tradition of personal talks, the form exemplified for so long by Alistair Cooke and still enjoyed by millions," he said.