Kenyan President Mwai Kibaki said it brought justice for al-Qaeda’s victims.
Some 224 people, mostly Kenyans, were killed in the twin bombings of the US embassies in Nairobi and in Tanzania’s main city Dar es Salaam in 1998.
Kenyan security services are now on high alert in case of revenge attacks.
Francis Kimemia, a senior official in Kenya’s internal security ministry, told the BBC that the US should also target al-Qaeda cells in East Africa.
The al-Shabab militant group, which controls much of southern Somalia, has close links to al-Qaeda and last year carried out a suicide bombing in Uganda.
In 2009 US forces killed Saleh Ali Saleh Nabhan, a top al-Qaeda operative accused of links to the 1998 embassy bombings, in a raid in Somalia.
“Osama’s death can only be positive for Kenya, but we need to have a stable government in Somalia,” Raila Odinga told Reuters news agency.
“The loss of its [al-Qaeda’s] leader may first upset the movement but then it will regroup and continue.”
Al-Shabab spokesman Mohamed Osman Arus said the group would take revenge for Bin Laden’s death with “destructive explosions”, reports the AP news agency.
But some Somali women’s groups thanked the US for killing Bin Laden, saying he was responsible for the deaths of thousands of women and children in the country, especially in the capital, Mogadishu, where al-Shabab has been battling the UN-backed government.
Somali President Sheikh Sharif Sheikh Ahmed also welcomed the US operation and said it would force al-Qaeda’s “hardline ideologies” into retreat.
However, he said he would have preferred him to have been captured alive and put on trial to answer for his crimes.
Tanzania’s President Jakaya Kikwete said the news was a relief but that the fight to bring the perpetrators of terror attacks to justice was far from over.
Bin Laden lived in neighbouring Sudan from 1991-6 but authorities in Khartoum have not yet commented.
The BBC’s James Copnall, in Khartoum, says Sudanese authorities are caught between trying to improve relations with the US and a domestic constituency which has some support for Bin Laden and even has fond memories of him.
Mali’s Foreign Minister Soumeylou Boubeye Maiga told the BBC that he welcomed Bin Laden’s death but said there is a risk of retaliation.
“We have to be careful – particularly in the next three to six months we have to be extremely vigilant – because we know that every time al-Qaeda suffers a blow like this, it’s followed by attempts at revenge,” he said.
Osama Bin Laden was killed by US forces in a ground operation in outside the Pakistan capital Islamabad, after the US received intelligence on his whereabouts.
US President Barack Obama said US forces had taken possession of his body.
Bin Laden was accused of masterminding a number of atrocities, including the attacks on New York and Washington on 11 September 2001.
He was top of the US’ “most wanted” list.
The US has put its embassies around the world on alert, warning Americans of the possibility of al-Qaeda reprisal attacks for Bin Laden’s killing.