UK Anti-Doping (UKAD) is probing alleged wrongdoing at Team Sky and British Cycling.
UK Anti-Doping (UKAD) is probing alleged wrongdoing at Team Sky and British Cycling, who share headquarters, and the package, delivered by British Cycling coach Simon Cope, forms part of its investigation.
Brailsford had previously refused to clarify exactly what the package contained, but he now says Sky's team doctor Richard Freeman told him it was Fluimucil, which is used for clearing mucus.
"Freeman told me it was Fluimucil for a nebuliser," Brailsford told the British government's Culture, Media and Sport committee during a hearing about doping in sport in central London.
"That was what was in the package. It was what Dr Freeman told me."
Brailsford said he had not been aware of the package's contents at the time, but had ascertained what was in it after mounting an investigation.
Quizzed as to why Sky had asked Cope to bring medical supplies to France from Manchester, rather than buying them locally, Brailsford said Cope had been flying out anyway.
"It may be where the whole situation has been slightly misled ... that the whole purpose of Simon Cope's trip to the end of the Dauphine wasn't to deliver a package. He was coming anyway," Brailsford said.
"He was coming and he was asked to bring something from the doctor's store."
Team Sky coach Shane Sutton and British Cycling president Bob Howden had earlier told the committee they did not know what the package contained.
The Daily Mail has reported the package was delivered on the day Wiggins won the Dauphine Libere stage race in France, giving him the biggest victory of his career at that point.
It has emerged Wiggins was granted therapeutic use exemptions (TUEs) to take banned anti-inflammatory drug triamcinolone before the 2011 Tour de France, the 2012 Tour, which he won, and the 2013 Giro d'Italia.
Five-time Olympic champion Wiggins, Cope, Brailsford and British Cycling have all strongly denied breaking anti-doping rules.
Brailsford said Wiggins's medical records have been given to UKAD.
Sutton, who stepped down from his role as British Cycling team director over sexism allegations earlier this year, said he was convinced Wiggins had not broken the rules.
"Knowing the kid (Wiggins) for many, many years, as far I'm concerned he never worked outside any rules," Sutton said.
"Given the fact Dave Brailsford was probably the pioneer behind clean cycling and created what is probably the cleanest team in the world -- he set up a zero-tolerance programme -- there was no wrongdoing there.
"I can't state strongly enough there was no wrongdoing on any part of Brad and Team Sky."
Australian Sutton appeared to become frustrated as the session progressed and at one point said he was "quite upset" Team Sky's integrity was being questioned.