He was the Spectator magazine's editor, when it carried an article which said "drunken fans" had "mindlessly tried to fight their way into the ground".
Apologising, he said he was glad a report "lays to rest the false allegation" about the fans' behaviour
The Hillsborough Families Support Group said it was "too little, too late".
Mr Johnson said: "I was very, very sorry in 2004 that the Spectator did carry an editorial that partially repeated those allegations, I apologised then and I apologise now.
"I do hope the families of the 96 victims will take some comfort from this report and that they can reach some sort of closure."
The Spectator article, which was not signed, was written in the wake of the death of British hostage Ken Bigley in Iraq, but went on to criticise "drunken" Liverpool fans at Hillsborough.
Mr Johnson said sorry at the time and went to Liverpool to reiterate his apology.
But Margaret Aspinall, chairwoman of the Hillsborough Families Support Group, who lost her son James, 18, in the tragedy, said: "What he has got to understand is that we were speaking the truth for 23 years and apologies have only started to come today from them because of yesterday.
"It's too little, too late.
"It's fine to apologise afterwards. They just don't want their names in any more sleaze. No, his apology doesn't mean a thing to me."

Pee Wee Pumps, which makes soft shoes for infants, describes its products as "cool" and "diva defining".
But pictures of the fashion range posted online have led to criticism on social media sites.
The shoes, which have collapsible heels and pointed toes, are available for infants up to six months old.
In the latest post on the company's Facebook page, an infant in heels sits astride a miniature motorbike with the caption: "This little #Diva, defining cool posing in her #PeeWeePumps."
The image was criticised by a number the site's users, who suggested it was "wrong" and "disgusting" to portray infants in such a way.
It comes amid growing concern at what is seen as the sexualisation of children.
"This is not ok," wrote Melissa Balinski.
Another commenter, Jen, said that "promoting products for babies this way is just sick".
Other promotional images for Pee Wee Pumps products include babies wearing bead necklaces, sequin dresses and tutus.
The range of shoes, which features styles made from red satin and leopard-skin material, have repeatedly met mixed responses from Facebook users.
"I will definitely avoid this brand," wrote Barrow, commenting on a picture of a baby in "black pump classics". "This is horrid," added Flory.
But some users left positive comments, remarking how the shoes made the infants "look adorable". "Too cute," wrote Latoyia.
The Pee Wee Pumps website displays a range of designs, labelled "Swanky", "Wild Child" and "Diva".
"She'll make a statement in this bold, red hue," reads the product description alongside a design labelled "Sassy".
The company came under fire earlier this month from UK campaign group Let Clothes Be Clothes, which posted images of the product range for infants with the warning "beware, the photos are shocking".
"I will definitely avoid this brand," wrote Owen. "That's disturbing. Even without the heels the pics would be not even remotely okay," wrote Eva.
Another user, Natasha, added to the campaign group's post: "Should be banned."
Pee Wee Pumps is based in Greensburg, Pennsylvania. The founder, Michele Holbrook, wrote in a statement on the company website that her products "are not intended for walking, but rather to meet the current and ever-growing popular demand for 'high-fashion' in infant apparel".

The host country beat South Africa by just two wickets at the match in Bristol.
England will now face either Australia or India at Sunday's final at Lords Cricket Ground in London.
Hopes will be high for England, who have only lost one match this competition and topped their table in the group stages.
London Mayor Boris Johnson has said he was "very, very sorry" for comments made in 2004 about Liverpool fans in the Hillsborough disaster.
[NEXT_CONCEPT]
A US footwear company has sparked outrage among consumers and campaign groups over a range of high heeled shoes for babies.
[NEXT_CONCEPT]
England have made it through to the final of the Women's Cricket World Cup.