The three American companies - Arconic, Celotex and Whirlpool - are facing 143 counts of wrongful death and product liability.
Arconic supplied cladding on the outside of the tower block, Celotex insulation was used in the cladding, and a Whirlpool fridge freezer was believed to have started the fire.
The building's cladding has been blamed for the rapid spread of the blaze, which killed 72 people at the tower block in west London.
The lawsuit on behalf of 69 who died and 177 who were injured in the fire is seeking "undetermined compensation, including punitive damages".
Lawyers for two US law firms said they have requested a jury trial in Philadelphia to hold the companies accountable.
Announcing the legal action at a press conference, Jeffrey Goodman of Saltz, Mongeluzzi, Barrett & Bendesky (SMBB) said: "Today we announce the filing of one of the largest product liability cases in history."
The lawsuit describes how the tower became a "flaming coffin" when the fire took hold on 14 June 2017.
Friday marks the two-year anniversary since the fire, but no criminal charges have been brought so far.
Lawyers involved in the US class action case say it could be more than two years before the case comes to trial.
Marcio Gomes survived the fire with his wife and two daughters, but his son Logan was later stillborn in hospital.
Speaking about the lawsuit, Mr Gomes said: "Corporations must be held to account for each and every person who died or was injured; from our son, the youngest person to lose his life, to the grandparents who died protecting the ones they loved.
"We will never forget. We will not let them down. We will see justice for all at Grenfell."
The husband of Maria del Pilar Burton, who survived the fire but died six months later in palliative care, said suing the companies in the US was the most effective way to hold them accountable.
Nicholas Burton said: "This is a wake-up call for all major corporations who behave as if they are above the law and refuse to face up to the damage they cause or change their ways, even after horrific disasters like the Grenfell Tower fire."
Last month, the government announced it had set up a £200m fund to replace unsafe Grenfell Tower-style cladding on high-rise buildings in England.
Some building owners have not yet taken action after the fire, with some trying to make leaseholders foot the bill for replacing the unsafe cladding.
Labour MP John Fitzpatrick told Sky News: "There are people living in tower blocks in the social and the private sector who need urgent action to make sure their homes are safe.
"Many private owners and private freeholders and developers are either dragging their feet or in complete denial and are hiding behind offshore titles."
A spokesman for Arconic said: "Arconic has no comment on any potential litigation. We continue to support the Public Inquiry and the investigations by the authorities."
A spokesman for Celotex said the company is "considering its position in relation to this action," and added the firm "remains committed to providing all relevant information to the Inquiry to assist it in its work".
A spokeswoman for Whirlpool said: "While the inquiry is ongoing, it would be inappropriate to comment further at this time.
"Separately, we would like to reassure owners of these products that they are safe and they can continue to use them as normal."