Kapoor will take over on September 1, while Becht is to remain as part time adviser to his successor and the board until September 2012 "to ensure a smooth transition," Reckitt said in a statement.
"After 16 years in the role, I believe now is the right time to retire," said Dutch national Becht, who at 54 is two years older than Kapoor.
Becht has led the group since its formation from the 1999 merger of Britain's Reckitt & Colman and Dutch group Benckiser, which he previously headed. He hit the headlines in 2009 after earning more than £90 million in stock options.
Kapoor expressed delight at his promotion and said he was looking forward "to leading the business to its next stage of growth and performance, supported by an excellent senior management team."
RB