Mr McAreavey, whose new bride was murdered on their honeymoon in Mauritius, tweeted on Friday evening: “Michaela was a vessel of love, courage and dignity.
“Hate can hurt, but never win.”
Two men involved in the video filmed at an event in Northern Ireland apparently celebrating the centenary of its foundation apologised after the clip emerged on social media.
In a statement, John Bell and Andrew McDade said it was a “matter of deep shame and regret” to have been involved in the broadcasting and singing about her murder.
They said that it was an “offensive, vile and wholly abhorrent chant”.
“This Facebook live video was not streamed with the intent of broadcasting any offensive chants whatsoever, rather it was generally broadcasting from the room.
“However, whether broadcast or not, the relevant chants should never have been sung either in public or private.
“We offer our sincerest and deepest apology to the Harte and McAreavey families, and indeed to wider society for our actions which whilst fuelled by alcohol, can neither be mitigated or excused in any shape or form.
“Our apology is unequivocal, and our acceptance of wrongdoing is absolute,” the two men said in a statement.
Ms McAreavey was murdered in her room at the Legends Hotel in Mauritius on January 10, 2011. She was 27 years old.
The teacher, who had married husband John 10 days earlier, was attacked after she returned to her room alone and disturbed a burglary.
In the statement, Mr Bell and Mr McDade added: “This incident is not reflective of who we are as people, nor more importantly of our respective families and friends.
“Several family members and friends have been subjected to online threats and abuse in recent hours due to our unacceptable actions.
“This is unfair and unwarranted; it is us and us alone who are responsible for our actions.
“In addition, this behaviour is unreflective of the values of the Loyal Orders and the wider unionist and loyalist community.
“Whilst it is scant consolation for the hurt our actions will have caused, we will write a formal letter of apology to the Harte and McAreavey families and make a confidential donation to a charity of their choice.”
It comes as Linfield Football Club has issued an apology. The Belfast club confirmed it has removed one of its voluntary coaches after their involvement in the video.
The person in question was a coach in the club’s girls’ academy.
“Linfield FC has today been made aware of a deeply offensive video in circulation on social media in which the involvement of a coach at our girls’ Academy can be clearly identified,” the statement read.
“The coach in question has been contacted and notified that his voluntary association with the club has been terminated with immediate effect.”
The club said they condemned the “offensive, sickening and deeply hurtful and insulting chanting” in the video and said they wished to “disassociate itself totally from the unacceptable behaviour”.
The statement added that the club “will not tolerate behaviour among any of our personnel that falls short of the standards that the club expects”.
"As has been illustrated on this occasion, the club will act swiftly and decisively against any individual whose conduct falls short of the standards that are required,” it added.
“Linfield FC apologises to the Harte/McAreavey families for the hurt that has been caused to them by the offensive actions of one of our now former coaches.”
Separately, the sand and gravel supplier Norman Emerson Group Ltd, which is based in Craigavon, Co Armagh, said they are investigating allegations the video was “allegedly made by one of our employees”.
In a statement, Norman Emerson Group Ltd said they had been “made aware” of the video and the apparent involvement of one of their workers.
"As a family and as a business, we endeavour to ensure an ethos of respect, inclusivity and consideration in everything we do,” they said.
"While we cannot control what anyone associated with us chooses to post online, such divisive and derogatory posts are in no way representative of who we are, and we unreservedly denounce such behaviour. We will not tolerate or condone sectarianism, bigotry, or intimidation in any form from anyone employed by us.
“Please be assured that a full and thorough internal investigation is underway.”
Taoiseach Micheál Martin said he was “appalled and horrified” by the video.
“We all remember that horrific murder of Michaela McAreavey,” he said. “It's beyond comprehension that people could behave in that manner and be so indifferent to the trauma that the family suffered.
“I think it speaks to the sectarianism and a degree of malice and hate in society that needs to be dealt with, and those involved in that should apologise in the first instance. The entire community and those involved should reflect very strongly on that.”
The Police Service of Northern Ireland (PSNI) and Orange Order have also confirmed that they are investigating the video.
Northern Ireland Justice Minister Naomi Long said she has raised the video with PSNI Chief Constable Simon Byrne, calling it “depraved”.
A PSNI spokesperson confirmed they are “aware of the video posted online” and are “examining the content to determine if any offences may have been committed”.
The Orange Order has also condemned those involved, calling the video “utterly abhorrent” and confirming they have “instigated an inquiry into the incident”.
They said if any of those involved are found to be members of the organisation, “they will face disciplinary proceedings”.
The online clip, which has been widely shared, references the woman going to “Mauritius on her honeymoon”.
Those singing go on to mock her death in the hotel room and reference the deceased woman’s father, the multiple All-Ireland winning Gaelic football manager Mickey Harte.
The video shows a group of men in a room of dozens of people, drinking, laughing, and chanting.
While it has not yet been verified where the scenes in the video took place, Orange Order banners appear to be visible in the background as well as Union flag bunting.
DUP leader Jeffrey Donaldson described it as “vile”, adding that it is “plain wrong and is deeply hurtful to the family of Michaela McAreavey”.
Former First Minister of Northern Ireland, Arlene Foster, added the footage was “just so wrong and hateful” and sent her love to Mrs McAreavey’s family.
Sinn Féin MP Michelle Gildernew expressed her outrage online, with the Fermanagh and South Tyrone representative confirming she has contacted the PSNI.
“Thank you to everyone who reported this to me tonight,” she wrote. “A beautiful young woman was murdered on honeymoon & this is how loyalists “celebrate” the Queen’s jubilee.
“I have reported this to the PSNI & will be taking further action.”
Ulster Unionist Party leader Doug Beattie described the video as “absolutely abhorrent, disgusting and shameful”.
South Belfast Alliance Party MLA Kate Nicholl said the scenes had shocked her.
"The hatred displayed in the video of men singing & laughing about the horrific murder of a young woman is incompressible. How her poor family must feel. I have reported to the police,” she tweeted.
Sinn Féin’s Linda Dillon added: “Wouldn’t dream of reposting the video doing the rounds because I have one beautiful wee girl and if that was my daughter my heart would be broken. My deepest thoughts are with the family. I am forever grateful my child is not capable of that kind of hatred.”
Mid Ulster MLA Patsy McGlone called the scenes “about as base in humanity as you can go – singing and laughing about the murder of an innocent young woman”.
SDLP Mid Ulster councillor Malachy Quinn added his condemnation, writing: “I was sent this video. I haven't the words to describe my anger at a song being sung mocking the murder of Michaela McAreavey, never mind it being sung at a ‘Centenary Event’.
“This is beyond reprehensible. Those involved should be bloody ashamed. I also can't describe the anger in my own community about this video.”
No-one has been convicted for the murder of Ms McAreavey.