They will share a $1-million award that comes with the prize.
The seminal discoveries represent a "paradigmatic shift in the fight against cancer", the Nobel committee said, since they do so not by targeting the tumor cells but by tweaking the immune system.
Allison and Honjo "showed how different strategies for inhibiting the brakes on the immune system can be used in the treatment of cancer", it said, adding that resulting treatments, known as immune checkpoint blockade, have "fundamentally changed the outcome" for some advanced cancer patients. Several such drugs have been approved for use in the US.
Allison and Honjo developed ways to unleash our T-cells - one of the major bodyguards of our immune systems.
"I'm still in sort of a state of shock, and this is all still sinking in", Allison said.
Allison studied a protein on T cells called CTLA-4 that acts as a brake on the immune system.
"Until the discoveries made by the 2018 Medicine Laureates, progress into clinical development was modest".
Tasuku Honjo Wins 2018 Nobel Prize in Physiology or Medicine
American and Japanese cancer researchers were presented the award for their groundbreaking discoveries in treating cancer.
Allison said scientists need to better understand "how these drugs work and how they might best be combined with other therapies to improve treatment and reduce unwanted side effects".
They winners will receive their prize from King Carl XVI Gustaf at a ceremony in Stockholm on December 10, the anniversary of the 1896 death of Alfred Nobel, who created the prizes in his last will and testament.
Allison was "elated" by the award, says his longtime friend and colleague Lewis Lanier, a professor and chair of the Department of Microbiology and Immunology at the University of California, San Francisco, who says he spoke with Allison just after the announcement.
"I was able to prove that it's not rare for fundamental research to lead to applications", Honjo said at a press conference held at the Japanese university in the city of Kyoto before the interview.
This type of therapy is a new approach in cancer treatment.
Honjo, also an immunologist, discovered a second receptor called PD-1 that also acted as a brake, but with a different mechanism of action. No literature prize is being given this year.
In December, Allison will be honored at the Nobel ceremonies in Stockholm - and he said that he looks forward to seeing fellow honoree Honjo in Stockholm, as well.
The Nobel in physics will be announced Tuesday, followed by the award for chemistry on Wednesday and the peace prize on Friday.
Mauricio Pochettino says Spurs' hectic fixture schedule is 'unfair'
When you're scoring as many goals as he is - 40, 50 or 60 goals a season - as a striker, I want to try and match that. They should fancy their chances, too. 'Barcelona might play better than Real Madrid did last season.