In a statement, the Taliban acknowledged Mansour's death for the first time and named his successor as Mawlawi Haibatullah Akhundzada.
Analysts say it is unlikely the group will change direction under Akhundzada, a religious scholar seen as hardline.
Last year the Taliban were plunged into turmoil when Mansour replaced the group's founder Mullah Mohammad Omar.
Mansour was killed in a strike on his car in Pakistan's Balochistan province on Saturday.
Under his stewardship the Taliban refused to take part in peace talks: instead, militant attacks escalated and became more daring.
Mawlawi Haibatullah Akhundzada, a former head of the Taliban courts, was a deputy leader to Mansour.