The money is part of a “New Deal” for what is widely regarded as a failed state, officials said.
Al-Qaeda-linked al-Shabab dismissed the meeting as “Belgian waffle”.
Al-Shabab is fighting to oust Somali President Hassan Sheikh Mohamud’s government, the first to be recognised by the US in more than 20 years.
The group controls most of southern Somalia, but it has been driven out of the main cities and towns, including the capital Mogadishu, by an African Union (AU) force backing the government.
The EU and Somali government believe now is a good time to adopt the programme as the country has entered a new era, with a more legitimate government and progress on the security front.
Mr Mohamud told the BBC Somali service he welcomed the New Deal.
“It’s a standard deal throughout the world in the post-conflict environment. This is a deal that is based on Somalia-led initiatives,” he said.
He said he would target four key priorities – security, legal reform, public finances and economic recovery, the AFP news agency reports him as saying.
EU Commission President Jose Manuel Barroso said the extra money would support a “new phase in the life of Somalia”.
The EU would give 650m euros, while the rest would come from countries such as Denmark, Germany, Sweden and the UK, he said.
The EU contribution would be in addition to the $1.6bn it gave Somalia from 2008 to 2013.
Most of this money was used to finance the AU force of some 18,000 troops, AFP reports.
The UK’s ambassador to Somalia, Neil Wigan, said the conference was “a major milestone”, the agency says.
The total of $2.4bn is more than double the amount diplomats were hoping to raise, it reports.
“Our combined efforts will maintain momentum and deliver the change that the people of Somalia desperately need,” Mr Wigan is quoted as saying.
The BBC’s Abdirahman Koronto in Brussels says some Somali government officials were disappointed that most donor countries were represented by low-ranking officials.
He says there is also some scepticism as previous pledges made at similar conferences have not been translated into improvements on the ground.
Al-Shabab said it expected donor pledges would remain mostly unfulfilled or the money would be lost in corruption.
“It’s a bit like Belgian Waffles: sweet on the outside but really has not much substance to it,” it said on its Twitter account.
Mr Mohamud said at a news conference that aid money had been used to save lives, and provide basic services to Somalis.
The New Deal would take Somalia from an “emergency to recovery” over the next three years, he said.
“This is a new chapter. Today we are ending a journey and starting a new one,” Mr Mohamud added.
There have been several international conferences to help Somalia rebuild itself, including one hosted by UK Prime Minister David Cameron in May.
The UK and other donors pledged some $130m in aid for Somalia at the time.
Earlier this month, Somalia’s government said international investigators it had appointed had cleared it of corruption allegations made by United Nations monitors.
In July, the UN Monitoring Group on Somalia said Somalia’s central bank had become a “slush fund” for political leaders and that the current governor played a central role in irregularities surrounding unaccountable disbursements of cash.
In September, Norway decided to directly pay government employees their salaries in order to curb corruption, UN-backed Somali Radio Bar-Kulan reported at the time.
Somalia is a good test case for the New Deal. It certainly fits the criteria for a fragile state, given that for six years in a row it has come top of the list of the world’s most failed states.
The New Deal focuses on peace and state-building. Without these, goes the argument, there can be no meaningful development, and aid money simply goes to waste. This has certainly been the case in Somalia, where billions of dollars have been thrown at a problem that refuses to go away.
The EU and Somalia argue that now is a good time to adopt the New Deal. They say the country has entered a new era, with a more legitimate government and progress on the security front.
But it is possible that the Brussels meeting will simply be the latest in the long list of expensive conferences on Somalia that end with ambitious communiques but have little or no impact on the development of the country.