The town is home to the prestigious Leander Club, which has trained more than 100 Olympic medal-winning rowers.
Prime Minister David Cameron previously said the plan was a "very good idea".
Royal Mail spokesman Simon Fellman said: "We're delighted to do it and we're pleased so many people are delighted about it."
The Royal Mail has painted more than 50 postboxes gold following Team GB's gold medal haul at London 2012.
Originally it said it was only painting them in "winners' home towns, or towns with which they are closely associated".
Town mayor Elizabeth Hodgkin said: "We are the home of rowing... I feel very excited about it.
"I think it's wonderful news, it's a great thing for the town."
Mr Fellman said: "It's almost like the torch has come again. It's a piece of the Olympics coming back to people's doorsteps.
"The support for the boxes, it's kind of like the new tourist attraction. It's fantastic and I think people have really taken it to their hearts."
The Henley-on-Thames postbox was painted on Friday.
The town is holding a victory bus parade for more than 24 Olympians on 25 August, along with a civic reception.
The Royal Mail has painted a postbox gold in the Oxfordshire town of Henley-on-Thames - in recognition of its medal winning rowing club.