A gothic horror novel, a Victorian murder mystery and a biography of the creator of modern environmentalism were also category winners.
The overall Costa book of the year will be revealed on 26 January.
Atkinson won the top prize in 1995 with Behind the Scenes at the Museum.
Other category winners include former teacher and librarian, Andrew Michael Hurley, who has won the first novel award for his debut, The Loney.
The gothic horror initially had a first print run of just 300 copies. The judges called it "as close to the perfect first novel as you can get".
Scottish poet Don Paterson won the poetry category for a second time for his "tour de force" collection titled 40 Sonnets. He last won the award 12 years ago.
Historian and writer Andrea Wulf won the biography award for The Invention of Nature: The Adventures of Alexander Von Humboldt, The Lost Hero of Science.
She tells the story of the visionary German naturalist whose ideas changed the way we see the natural world and created modern environmentalism.
Young adult fiction and children's writer Frances Hardinge won the children's book award with The Lie Tree, a Victorian murder mystery.
The five Costa book award winners each win Â£5,000 and are all now in the running to win the Costa book of the year.
It is the only major UK book prize that is open solely to authors resident in the UK.
Last year's Costa book of the year went to Helen Macdonald's H is for Hawk. In 2013 it was The Shock of the Fall by Nathan Filer and in 2012 it was Bring Up the Bodies by Hilary Mantel.

Four attackers were seen entering the office, followed by heavy gunfire and several explosions.
Five security officers - including a police chief - were among the dead and 26 government officials among the hurt.
A spokesman for the Taliban said they carried out the attack.
The siege ended seven hours after it began and all four gunmen were killed by the Afghan National Security Forces which had surrounded the area.
Police said they rescued the attorney general from his office, which is just 200m (650ft) from the office of the governor of Balkh province.
The governor's aide told the BBC that the governor, Atta Muhammad Nur, was at home when the attack began but was taken to his office to monitor the situation.
In a statement seen by the BBC, Taliban spokesman Zabihullah Mujahid said: "Breaking News: This noon suicide [attackers] stormed office of the attorney and appeal court of Balkh province. Heavy casualties for enemy, battle continues."
The Taliban has targeted Afghanistan's legal system in the past. In June 2013, the group detonated a car bomb in front of the compound of Afghanistan's Supreme Court, killing 17 and wounding 39.
And in December of 2014, Atiqullah Raufi, the chief of the secretariat of Afghanistan's Supreme Court, was assassinated by Taliban gunmen in the west of Kabul.
The attack in Mazar-e-Sharif comes a day after an American soldier was killed in a fire fight between US and Afghan troops in eastern Afghanistan.
Kate Atkinson has won the Costa novel award for the second time in three years for A God in Ruins - the companion novel to Life After Life, which won the award in 2013.
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Gunmen dressed in military uniforms have stormed the office of the attorney general in the northern Afghan city of Mazar-e-Sharif, killing at least 10 people and injuring more than 65.