The Federal Court judge found it contained three defamatory meanings - that Dr Chau bribed former UN president John Ashe, was part of a plot to bribe him and acted in so seriously wrong a manner as to deserve extradition to the United States on criminal charges.
He was not satisfied it conveyed a fourth meaning that Dr Chau created his Australian business empire by making illicit payments to government officials.
Dr Chau welcomed the decision, saying his faith in the Australian legal system had been vindicated.
"I will be donating the damages awarded by Justice Wigney in full to a number of charities supporting Australian veterans and their families," he said in a statement.
Fairfax and Garnaut had denied the article insinuated "actual guilt", saying it suggested he was strongly suspected of being involved in the scandal.
If the judge found the alleged defamatory meanings were conveyed, Fairfax relied on the defence of qualified privilege - submitting the article was of legitimate public interest and it acted reasonably.
The judge found the article went beyond simply conveying a suspicion that Dr Chau had bribed Mr Ashe.
"Rather, by a combination of disparagement, insinuation and suggestion, it effectively imputed guilt," he said.
While the article contained Dr Chau's apparent response to, or denial of, some aspects of the allegations, the manner in which they "are disaggregated and inserted in the narrative undermines their effect".
"There is a general tone of incredulity in relation to the denials."
He rejected the defence raised by Fairfax and Garnaut, finding their conduct had been unreasonable in a number of ways.
In assessing damages, the judge said he took account of evidence showing the personal distress and hurt suffered by Dr Chau and evidence establishing his good reputation prior to the publication.
"Given his previously unblemished reputation, and his position and profile, it was important for the award of damages to be such as to send a strong signal to the public of the vindication of Dr Chau's reputation."
The Sydney Morning Herald and The Age later said in a statement that the decision would be appealed.
"We are disappointed that the judge did not uphold our public interest defence, which was the only one available to us under Australian defamation law, and was not persuaded by our evidence," the statement said.