The 75-year-old, from London, admitted the abuse of 11 boys as young as eight. He denied three other offences.
Denning, who was arrested in a police inquiry into the Walton Hop Disco for teenagers in Walton-on-Thames, Surrey, will be sentenced on 6 October.
He was part of the original line-up that launched Radio 1 in 1967, but left two years later.
The prosecution said it did not intend to proceed with a trial on the three charges to which Denning had pleaded not guilty.
He is currently serving a 13-year jail term for sexual assaults against 24 victims aged nine to 16 from the 1960s to 1980s.
He will be sentenced at Southwark Crown Court by the same judge who jailed him for those offences in 2014.
The latest offences Denning admitted included indecent assaults on men and boys and inciting boys aged under 16 and 14 to commit acts of gross indecency.
The offences he denied were three counts of indecent assault.
Surrey Police said the case against the former DJ formed was part of its Operation Ravine investigation into non-recent sexual offences linked to the Walton Hop Disco which ran between 1958 and 2001.
Det Ch Ins Jo Hayes said: "Denning, who was looked up to and sometimes idolised by many young people, has used his status to prey on innocent children which he has now admitted to."
Four of Denning's victims were in court to see him plead guilty.
Det Ch Insp Hayes said: "The four boys who Denning abused had moved on with their lives and were now adult men with families and careers. Often, they had not spoken to those closest to them about their ordeal as a child and only recently, as part of this investigation, have been able to do so...
"We can never go back and take away the abuse these four men suffered as boys but I hope, in some way, today's guilty plea brings some closure for them."
Chris Denning rose to prominence in the 1960s on BBC television and radio.
He was one of the first announcers heard on BBC Two when the channel began broadcasting in 1964 and went on to be one of the original Radio 1 DJs.
Denning helped launch the careers of the Bay City Rollers and Gary Glitter, and ran his own music and video production business.
He remained a well-known DJ and presenter into the early 1970s.
The allegations that led to his conviction in 2014 arose after the sex abuse perpetrated by late Radio 1 DJ Jimmy Savile came to light.
Denning's arrest was under the strand of the investigation into offences not connected to Savile, but the court heard he did use his fame to "entice" boys.
This included taking some victims to recordings of Top of the Pops, and in other instances, introducing them to celebrities including Savile.
Denning had a number of previous convictions for abusing young boys.
In 1974, he was convicted of gross indecency and indecent assault but was not imprisoned.
He was then jailed for 18 months in 1985 for gross indecency, and in 1988 he received a three-year sentence, this time for indecent assault and possession of indecent images.
In 1996, he was handed a 10-week sentence for publishing indecent articles.
He was arrested in the Czech Republic in 1997 and eventually jailed in 2000 by a Prague court for four and a half years for having sexual contact with underage teenage boys.
The UK tried and failed to have Denning extradited from the Czech Republic, but in 2005 he was arrested at Heathrow Airport, having arrived from Austria.
In January 2006, a British court jailed him for four years after he admitted five charges of indecent assault on boys under 16 during the 1970s and 80s.
He was then extradited to Slovakia, where he was given a five-year sentence in 2008 for producing indecent images of children.
Former BBC DJ Chris Denning has pleaded guilty to 21 child sex offences committed between 1969 and 1986.