The 1,111-carat stone was recovered from its Karowe mine, about 500km (300 miles) north of the capital, Gaborone.
It is the biggest diamond to be discovered in Botswana and the largest find in more than a century.
The 3,106-carat Cullinan diamond was found in South Africa in 1905 and cut into nine separate stones, many of which are in the British Crown Jewels.
"The significance of the recovery of a gem quality stone larger than 1,000 carats, the largest for more than a century... cannot be overstated," William Lamb, the CEO of Lucara Diamond, a Canadian diamond producer, said in a statement.
Lucara says two other "exceptional" white diamonds - an 813-carat stone and a 374-carat stone - were also found at the Karowe mine.
"This has been an amazing week for Lucara with the recovery of the second largest and also the sixth largest gem quality diamonds ever mined," Mr Lamb said.
The stone is yet to be evaluated, but commodities and mining analyst Kieron Hodgson, told AFP news agency that "the potential to be one very expensive diamond."
In April a flawless 100-carat diamond was sold for $22.1m (£14.8m) at Sotheby's in New York.
The gem, originally mined in South Africa, had taken more than a year to cut, polish and perfect.
Botswana is the world's largest producer of diamonds and the trade has transformed it into a middle-income nation.