TOTP as it is also known, was once the must-see program for music fans but has suffered from dwindling ratings in recent years.
A switch from BBC1 to BBC2 and a relaunch proved unsuccessful so the final half-hour show will go out on July 30.
"The decision to bring the show to an end after 42 years has not been taken lightly and over the past few years every effort has been made to maintain the quality and distinctiveness of the show," BBC director of television Jana Bennett said in a statement.
"However the BBC's Creative Review Music Strategy has concluded that in a rapidly changing musical landscape, Top of the Pops no longer occupies the central role it once did."
Ms Bennett said the show has faced "ever-increasing competition" in recent years from the internet, 24-hour music channels and other outlets whose flexibility and accessibility meant TOTP could no longer compete.
BBC television had also expanded the type and amount of music it covers on its two terrestrial channels, BBC1 and BBC2, as well as its free-to-air cable stations, BBC3 and BBC4, she added.
TOTP2, an archive show based on Top of the Pops' back-catalogue, will continue and may include some new performances as well as one-off specials.
Top of the Pops first aired on New Year's Day 1964, with the Rolling Stones performing "I Wanna Be Your Man". The Beatles were number one in the chart with "I Want to Hold Your Hand".
The show had its heyday in the 1970s with 15 million viewers each week.