Sheikh Jassim bin Hamad Al Thani, chairman of one of Qatar's biggest banks, has also tabled a bid.
The Glazer family are considering selling the club and a 'soft deadline' of Friday had been set for proposals.
Ineos said it wants to make the club a "beacon for a modern, progressive, fan-centred approach to ownership".
In a statement confirming its bid for the 20-time English champions, the company added: "We would see our role as the long-term custodians of Manchester United on behalf of the fans and the wider community.
"We are ambitious and highly competitive and would want to invest in Manchester United to make them the number one club in the world once again."
It added: "We also recognise that football governance in this country is at a crossroads. We would want to help lead this next chapter, deepening the culture of English football by making the club a beacon for a modern, progressive, fan-centred approach to ownership.
"We want a Manchester United anchored in its proud history and roots in the North West of England, putting the Manchester back into Manchester United and clearly focusing on winning the Champions League."
The Ineos group, owned by 70-year-old British billionaire Ratcliffe, has a history of investment in sport and owns French Ligue 1 club Nice and Swiss Super League club Lausanne.
Its sporting portfolio also includes high-profile sailing team Ineos Britannia, led by Sir Ben Ainslie, which is aiming to win the 2024 America's Cup for Great Britain.
Ineos also has a five-year partnership with Formula 1 team Mercedes and took over British-based cycling team Ineos Grenadiers (formerly Team Sky) in 2019.
Ratcliffe made an unsuccessful late £4.25bn offer to buy Chelsea last year when Russian owner Roman Abramovich put the London club up for sale.
Ratcliffe - born in Failsworth, Greater Manchester - is a boyhood fan of United and one of the UK's richest men. His personal wealth is estimated at somewhere between £11bn (Forbes) and £6bn (Sunday Times), which makes him the 27th wealthiest person in the UK on the Sunday Times Rich List.
His petrochemicals firm Ineos makes about £50bn in annual sales and employs more than 26,000 people across 29 countries.
Following his failure to acquire Chelsea, Ratcliffe said he would have tried to buy United but, after meeting with brothers Joel and Avram Glazer, he stated that they did not want to sell - a stance that has now changed.
At least two offers for United from the United States are expected, while there have also been suggestions of interest from Saudi Arabia.
That means there could be up to five parties trying to negotiate a full sale, with others looking to make a smaller investment in return for a partial stake in the club.
The Glazer family have owned United since 2005 and in November confirmed they wanted to "explore strategic alternatives" for the club.
Sheikh Jassim's Qatari consortium has promised to "return the club to its former glories".
It added: "The bid will be completely debt free via Sheikh Jassim's Nine Two Foundation, which will look to invest in the football teams, the training centre, the stadium and wider infrastructure, the fan experience and the communities the club supports.
"The vision of the bid is for Manchester United to be renowned for footballing excellence, and regarded as the greatest football club in the world."
Described as a life-long Manchester United fan, Sheikh Jassim is chairman of Qatari bank QIB and the son of a former prime minister of Qatar.
Concerns have been raised about a Qatari bid by human rights group Fair Square and Manchester United LGBTQ+ fan group Rainbow Devils.