Rebecca Morgan, director of commemorative coins at the Royal Mint, said it was the first time the design of the 5p coin had changed since 2008.
She said it “represents the deep connection between our monarchy and the natural world” and reflects the King’s “lifelong dedication to environmental conservation”.
The eight post office branches have been chosen because they either have “oak” in their name or are close to famous oak trees.
The 5p featuring the King is the third denomination to enter circulation, after the 50p and £1 coins bearing his likeness.
Only about 0.2% of the 24.6 billion coins in circulation in the UK bear his portrait, with the rest featuring his mother Elizabeth II.