A shorter runway could have limits on its use, although Arora Group insisted it would be able to accommodate aircraft of all sizes.
The announcement means that for the first time, there will be two bids on the table to build a third runway at Heathrow.
Arora Group said its plan, called Heathrow West, could have a new runway fully operational by 2035, while a new terminal would open in two phases, in 2036 and 2040.
The plan, developed with infrastructure company Bechtel, has a cost estimate of under £25 billion, not including the redevelopment of the airport’s existing central area.
Heathrow said in 2018 it could complete its runway for £14 billion, but it is now expected to cost billions more.
In June, the government invited competing proposals, external for Heathrow’s expansion and set a deadline of 31 July.
Mr Arora, who is one of the largest landowners at Heathrow, said: “After a decade working with our world-leading design and delivery team, I am very proud that the Arora Group can finally unveil to the UK government our Heathrow West proposal.
“The Arora Group has a proven track record of delivering on-time and on-budget projects including in and around Heathrow airport.
“We are delighted that the government has taken a common-sense approach to invite proposals from all interested parties for the very first time rather than granting exclusivity to the current airport operator, no matter its track record.”
Mr Arora has repeatedly accused the airport of wasting money.