Webber will line up for Porsche in the World Endurance Championship.
Horner says Red Bull supports Webber's decision.
"I am sure Mark thought long and hard before making what has no doubt been a very difficult decision," said Horner.
"His achievements in Formula One are extensive and I am sure he will continue to push hard and build on that record until the end of the season. We support Mark’s decision, he has been an excellent addition to the team since joining us in 2007 and we wish him all the best in the next stages of his career."
Red Bull has not yet decided on who will replace Webber at the team.
A decision on who will partner Sebastian Vettel in 2014 will be made later in the season.