Three judges at the High Court handed out the penalties to the publishers of the two tabloid newspapers.
The Lord Chief Justice, Lord Judge, sitting in London with Lord Justice Thomas and Mr Justice Owen, ruled that the newspapers breached contempt laws in reports about Miss Yeates’s landlord, Christopher Jefferies.
Attorney General Dominic Grieve, who brought contempt proceedings and told the judges that reports would have posed a “substantial risk” of prejudicing any trial Mr Jefferies might have faced.
Both newspapers had disputed Mr Grieve’s allegations and denied contempt.
Earlier, Mr Jefferies accepted substantial undisclosed libel damages from eight newspapers over allegations made against him over Miss Yeates’s death in December 2010.
After the hearing, Mr Grieve said: “It was an extraordinary case. When Mr Jefferies was arrested these two newspapers completely lost the plot.
“They just went on this extraordinary frolic, vilifying Mr Jefferies in a way that was, frankly, outrageous.”
Mr Grieve said the level of fine was not as important as the “message” sent out by judges.
Lord Judge had said there was no doubt about the identity of the man who killed Miss Yeates “or that Mr Jefferies is innocent of any involvement in it”.
He added: “By way of emphasis, he is not simply presumed in law to be innocent of the killing. As a matter of fact and reality he is innocent. He is not facing trial, and will never face trial.”
However, at the time the articles were published he was under arrest and proceedings against him were active.
“No one was to know that before very long he would be entirely exonerated,” he added. “That feature makes this an unusual case.”
Judges had reserved judgment at a hearing in London earlier this month.
Miss Yeates, 25, who lived in Clifton, Bristol, disappeared on December 17, 2010, after going for Christmas drinks with colleagues. Her frozen body was found on a roadside verge in Somerset, on Christmas Day.
Mr Jefferies, a retired teacher in his 60s, was arrested on December 30. He was subsequently released without charge and was “entirely innocent of any involvement”, Mr Grieve told judges.
A 33-year-old engineer has admitted killing Miss Yeates.
Dutchman Vincent Tabak has pleaded guilty to manslaughter but denies murder.
Tabak, who lived next door to Miss Yeates, is due to go on trial accused of murder at Bristol Crown Court in October.