It is by far the highest fine for any environmental offence in British history.
Four other big companies have also been penalised for underestimating greenhouse gas emissions from plants in Scotland. They are the Dow Chemical Company, Tennent Caledonian, Pernod Ricard and FMC BioPolymer.
The fines were levied by the Scottish Environment Protection Agency (Sepa) for breaches of the Europe Union's Emissions Trading Scheme. This is the EU's main tool for cutting pollution, and it relies on companies accurately reporting emissions.
This is the first time that Sepa has imposed such penalties, and the size of the fine on ExxonMobil has stunned observers.
Previously, the largest fine for an environmental offence was the £1m that another oil company, Shell, had to pay for polluting the River Mersey in 1989.
Firms found guilty of misreporting their greenhouse gas emissions can be fined €100 (£83) for every tonne they miss: fines are now levied in euros. ExxonMobil was found to have missed 32,966 tonnes of emissions from its Mossmorran ethylene cracker plant in Fife in 2008, and was fined €3.296 million or £2.738m.
The fine was imposed in 2010-11, but was only just been revealed by Sepa. The money was passed to the Scottish Government, which used it to fund a series of environmental projects including low-polluting buses, peatlands restoration and boosting energy efficiency in buildings.
ExxonMobil has also been fined £844,765 for underestimating climate pollution from its Esso oil refinery at Fawley, near Southampton in the south of England. In a statement, the company said it regretted the errors it had made.
"Inaccuracies were identified by ExxonMobil's internal systems and were immediately reported to the regulator by the company," said a company spokesman. "We have now fully reviewed and improved our procedures at both sites to address the issues we identified."
The root cause of the problems at Mossmoran was "incorrect mapping of routings within facilities", he said. The missed emissions amounted to less than 5% of the site total, which was being reduced by "significant investments" from the company.
The reaction from environmentalists was scathing. "It is very embarrassing for a company as well resourced as ExxonMobil to have to admit that they can't fill in forms properly," said Dr Richard Dixon, director of WWF Scotland.
"The whole point of the European trading scheme is to limit the total climate pollution coming from industry, so it is quite right that fines should be high for those who fail to comply. This massive fine is a big message to others to get it right."
Sepa pointed out that Exxon's penalty was a "mandatory consequence" of breaching the Emissions Trading Scheme, although there was "no direct environmental impact". Scottish ministers accepted that it was a genuine error and that there had been "no intention to mislead".
The US chemicals giant, Dow, was fined £37,000 in August 2011 for wrongly reporting emissions from its factory in Grangemouth. The company said this was because it had omitted to include pollution from a canteen boiler, and it now "fully understands its reporting requirements".
The lager company, Tennent Caledonian, is currently facing a fine of £30,390 for failing to report emissions from its Wellpark brewery in the east end of Glasgow. According to the company, this was a "technical breach" of emissions from three small boilers and the site "has been compliant in all other aspects of its environmental obligations".
The two other companies fined in 2011 were the French drinks corporation Pernod Ricard, for breaches at its Strathclyde whisky distillery in Glasgow, and the US food and pharmaceuticals company, FMC BioPolymer, for breaches at its Ladyburn chemical works in Girvan. They could not be reached yesterday.
Pernod Ricard, however, has previously pointed out that it has cut greenhouse gas emissions from its Strathclyde distillery by 5800 tonnes. By investing in better controls it was able to produce 11% more whisky without increasing energy use.