The company behind Durex condoms and Enfamil infant formula said Kapoor, 60, would leave by the end of 2019 after more than eight years at the helm and more than three decades with the company overall.
Reckitt has begun looking for a successor and will consider internal and external candidates.
Indian-born Kapoor is the latest consumer industry chief to hand over the reins in difficult times, marked by slower growth, little pricing power and changing consumer habits.
Unilever, Campbell Soup, British American Tobacco and PepsiCo have all named new bosses in recent months, continuing the march of a new generation of consumer CEOs tasked with rekindling growth as traditional players fight back against media-savvy upstarts.
Reckitt, which Kapoor sought to transform from a British household cleaning company into a global consumer healthcare leader, has faced unique problems over the past three years.
Performance was dented by a failed product launch, a cyber attack, a safety scandal in South Korea and a temporary baby milk factory shutdown in the Netherlands.
Furthermore, Kapoor spent $17 billion in 2017 buying U.S. baby formula maker Mead Johnson, which was struggling and has since divided opinion. It dramatically boosted the company's presence in fast-growing China, but also took it into the new and highly competitive area of baby formula.
TWO BUSINESSES, ONE PARENT
Kapoor was also the architect of a plan designed to split the firm into two stand-alone business units, one focused on health and the other on home and hygiene, but under the same parent company. The new structure, dubbed RB 2.0, is due to be completed in 2020.
"I think he had a plan to retire but in acceptance of underperformance on his watch, he may have brought that plan forward," said Liberum analyst Robert Waldschmidt.
Reckitt shares lost more than 4 percent, underperforming a host of other UK exporters that fell following the defeat of the government's Brexit deal.
"The announcement ... compounds our sense of unease around RB," said Jefferies analysts. "A feeling that the success model is finding its limits and that the loss of Pfizer has been a mortal blow."
Kapoor pulled Reckitt out of last year's bidding for Pfizer's consumer health assets, a deal seen by many as an obvious culmination of years of feasting on smaller healthcare assets.
Another analyst on Wednesday linked the share price fall with the possibility that a new CEO could decide to limit profit margins in order to invest in boosting revenue growth.
"We think it's likely that the threat of a margin reset could spook investors and put pressure on the share price," RBC Capital Markets analysts said.
Jefferies analyst Martin Deboo said it was tough to say who could succeed Kapoor, given Reckitt's custom of keeping second-tier managers out of the spotlight, and a unique corporate culture that can make it hard for outsiders to integrate.
He said Rob De Groot, president of the hygiene and home division, must be a lead contender, while market speculation included Stefan Heidenreich, who recently stepped down as CEO of Germany's Beiersdorf.
Kapoor, who grew from humble beginnings in the north Indian city of Bareilly, has overseen a near doubling in Reckitt's market value to 44.3 billion pounds as of Tuesday, spending heavily on acquisitions.
Kapoor had his pay cut twice in the past two years, due to company underperformance and a measure of investor dissatisfaction with a 25.5 million pound package in 2015 that made him Britain's third-highest paid boss.
Reckitt's value almost doubles under CEO Kapoor -
(Additional reporting by Noor Zainab Hussain in Bengaluru; Editing by David Evans and Keith Weir)
By Noor Zainab Hussain and Martinne Geller