It follows the release of a report into the disaster which resulted in the death of 96 fans.
Kelvin MacKenzie wrote the headline The Truth on the front-page story which ran four days later.
Trevor Hicks, of the Hillsborough Families Support Group, said it was "too little, too late".
In a statement Mr MacKenzie said: "Today I offer my profuse apologies to the people of Liverpool for that headline.
"I too was totally misled. Twenty-three years ago I was handed a piece of copy from a reputable news agency in Sheffield in which a senior police officer and a senior local MP were making serious allegations against fans in the stadium.
"I had absolutely no reason to believe that these authority figures would lie and deceive over such a disaster.
"As the prime minister has made clear these allegations were wholly untrue and were part of a concerted plot by police officers to discredit the supporters thereby shifting the blame for the tragedy from themselves.
"It has taken more than two decades, 400,000 documents and a two-year inquiry to discover to my horror that it would have been far more accurate had I written the headline The Lies rather than The Truth.
"I published in good faith and I am sorry that it was so wrong."
The former editor of the Sun has offered "profuse apologies to the people of Liverpool" for blaming fans for the Hillsborough tragedy.