Richard Francis Burton and John Hanning Speke set out in June 1857 to discover the source of the River Nile. That quest had intrigued Herodotus, who believed the river issued from a bottomless cavern, and beguiled Alexander the Great, who assumed its waters flowed from India. Ptolemy claimed that the Mountains of the Moon hid the river's headwaters. As late as 1857, the Nile's source was the most conspicuous gap in the global map which fascinated Britain's Royal Geographical Society.

Despite the romance, drama and tragedy which enveloped the 1857 expedition, identifying the source of the Nile was intrinsically pointless. Cataracts, jungles, diseases and marshes meant the river could never be used as a commercial highway to open up East Africa. Its mercantile value was trivial compared, say, with the boundless potential revealed by those voyageurs who connected America's Great Lakes with the Mississippi River. As long as the Nile continued each year to flood Egypt's fields, why did it matter which central African lake the river flowed out of?

Candice Millard has previously written two excellent works of history, one about a presidential assassination (Destiny of the Republic), the other about a jejune war correspondent later to become Britain's Prime Minister (Hero of the Empire). She has also published one quite exceptional book, The River of Doubt, chronicling Teddy Roosevelt's nearly fatal, post-presidential voyage down a tributary of the Amazon.

Millard's great gift is total immersion, a combination of intense scrutiny of available documentation and a capacity to place herself in the setting of the story and the thinking of her characters. Those skills lay a foundation on which Millard deploys her remarkable capacity for telling gripping, moving stories.

Burton and Speke offer rich pickings for talents like those. Both kept copious journals, on which Millard draws throughout, without ever losing her critical intelligence and discernment in extracting the truth among what the explorers claimed. As she did in describing the floor of the Amazon rainforest, Millard evokes the natural world with flair and sympathy. In her Africa, elephants need fear only "the miniscule creatures teeming at their feet". Slave drivers spitting out seeds can create a shaded track of mango trees along their "path of human misery". At one stage Millard imagines the explorers' route laid out "like a modern-day satellite picture".

As for the explorers, their equipment turned "damp, dripping, rotten or rusted". Even their bodies degenerated into "limping, coughing, shivering shells". While Burton was paralysed for much of a year, Speke went blind for a while and lost hearing after a beetle chewed its way into his ear. Both explorers became more than a little mad. Although neither man was especially skilled at cartography or scientific measurement, both were fearsomely gifted at nurturing a grudge.

Burton was a pornographer, a master fencer proficient in 25 languages, a furtive visitor to Mecca and the founder of the Cannibal Club. Imagine Bear Grylls crossed with David Attenborough, with a dash of someone more louche and lustful tossed into the mix. Millard maintains that Burton "felt at home in any land but England, studying any language and culture but his own". Bram Stoker found Burton "dark and forceful and masterful and ruthless", and his taste for gothic excess impelled him to create Dracula.

Speke, Burton's "opposite in every way", was more prissy but still more vengeful. He loved shooting anything and everything, survived 11 stab wounds after one melee (when a spear impaled itself in Burton's cheek), and espoused arrogantly ignorant racist views. Together, they provide abundant raw material for multiple biographies, a mediocre film (Mountains of the Moon, 1990) and this engrossing new account.

If readers tire of Burton and Speke, then Millard has exhumed the tale of Sidi Mubarak Bombay, a former slave turned diligent and loyal guide who proved indispensable to both men. Having taken the British to two of Africa's Great Lakes, Bombay later traversed Africa from East to West. After judicious appraisal of his record, Millard concludes that Bombay "accomplished more than any single explorer ever to enter the continent". Bombay, rather than his two English wards, deserved medals and portraits, as well as a decent living wage.

Millard ends her narrative with Speke shot dead and Burton withered away, left with "no-one to fight and nothing to fight for". Readers tantalised by the story might seek out a copy of Richard Hall's splendid Lovers on the Nile (1981), which chronicles the rambunctious adventures of Sam Baker and the intrepid wife he acquired in a Balkan slave market. For those suspicious of imperialist ventures, Millard reminds the reader of Dr Johnson's observation: "I do not wish well to discoveries for I am always afraid they will end in conquest and robbery".