The election, which was reported on Thursday, has not been officially confirmed by the Taliban. But a commander present at the meeting to elect Mansoor confirmed the report to Reuters news agency.
Reports said the election was held in Pakistan's city of Quetta.
The news comes as a Taliban representative and the group's Twitter account confirmed the death of Omar, Reports said. However, the group refused to give information where and when Omar had died.
Mansoor will be only the second leader the Taliban have had since Omar, an elusive figure rarely seen in public who founded the group in the 1990s.
In an interview with Al Jazeera, Yehia Ghanem, a journalist who covered the Taliban for years, said the way Mansoor's election was announced, "it is obvious that it is true."
Mansoor is a "key figure" in the Taliban organisation, serving as the governor of Kandahar before the American invasion, he said.
"He actually led many intelligence operations, very important and major ones, in which he beat the biggest intelligence apparatus in the world," Ghanem added.
Mansoor's leadership and intelligence experience in Kandahar, the birthplace of Taliban, make him a logical successor of Omar, he added.
The Afghan government said on Wednesday that Taliban leader Omar died more than two years ago, in a hospital in Karachi. Ghanem, however, said that the report was "doubtful."
Following the announcement, a second round of peace talks between the Taliban and the Afghan government have been postponed.
Bloom Gist was told, however, said that despite the postponement of the talks, the Afghan government is optimistic that Mansoor would be more open to negotiations.
Still, our correspondent said that the Taliban has also been carrying out attacks across the country, taking control of more territories from the government as recently as last Wednesday.
