Ms Brimble died in September 2002, less than 24 hours after she boarded a P&O cruise ship for the holiday of a lifetime.
A coronial inquest spanning 16 months led to charges being laid against Wilhelm, in whose cabin she was found.
He was charged with manslaughter and supplying the illegal drug GHB, also known as fantasy or liquid ecstasy, which was found in her system.
But last year, after a four-and-a-half week trial, a jury in the NSW Supreme Court failed to reach a verdict.
Drug supply charge
On Monday, as his second trial was due to begin, Wilhelm pleaded guilty to an alternative charge to manslaughter, saying that he caused Ms Brimble to take the drug.
But Justice Roderick Howie refused to accept the plea.
"I cannot allow him to plead guilty to a matter he did not commit, and he did not commit this," Justice Howie said.
On Wednesday, crown prosecutor Terry Thorpe said the manslaughter charge against Wilhelm would therefore be dropped.
"Can I say, I wholly support the decision that's been made," Justice Howie said.
Wilhelm later pleaded guilty to a drug supply charge. He will be sentenced on April 29.
