The 50-year-old had been subject to an internal investigation for alleged ‘inappropriate behaviour’ towards a female colleague as first reported by Dutch media.
Red Bull believe that the investigation was ‘fair, rigorous and impartial’ and following the breaking news, the Sky Sports F1 crew had their say on the decision.
Speaking in Bahrain ahead of the first race of the season, Brundle described the ordeal as ‘curious business, but that Red Bull have made their findings clear.
"That statement from Red Bull GmbH is drawing a solid line underneath the whole thing. That appears to be their position,” he said.
"It does say they complainant can take further action against this but they are clear. They have done a deep investigation and talked for hours, many pages of documents have been generated, so clearly there was something to talk about.
"Christian Horner has always strenuously denied all wrongdoing on this and they are literally like 'case closed and complete'.
"I find this a very curious business. We knew no facts whatsoever about this story, lots of echoes, lots of rumours that swirl around.
"We can only go by that statement and it looks like a line drawn underneath it and let's see if anything else comes out of that from third parties."
Hill: Now they carry on
1996 world champion Hill echoed that the team are confident that Horner is innocent.
"There will be people who say that it’s the organisation judging itself and not being exposed to any other external influences,” he added.
"They had to investigate an allegation and they’ve satisfied themselves that their man is in tact and that they’re going to carry on."
Noami Schiff stressed that this investigation cannot loom on any further that it already has: "Red Bull is huge company,” she said.
“It's a corporate matter. An investigation has been handled, whether it be independent or not, you would think and assume they take this with the upmost seriousness and handle it completely fairly.
"It comes at the risk of going completely wrong if it's found out that it's not the case. So, I believe they have done everything they can.
"What they say in the statement is super important. There is a level of discretion that needs to be kept because it involves the private life of people, that doesn't need to be exposed to the world.
"So, we just hope that this is clear and it won't go any further unless it has to, but you don't want this looming over the sport and the credibility of these people."