He admitted 29 charges involving boys as young as nine when he appeared at Southwark Crown Court in London. But he denied a further 12 charges and will face trial on November 24.
The offences he admitted were committed between 1967 and 1984 and involved boys aged from nine to 16.Denning, 73, of Basildon in Essex, was one of the original Radio 1 line-up and was the first announcer heard on BBC2 in 1964.
He was first arrested by detectives from sex crime inquiry Operation Yewtree in June last year.
Judge Alistair McCreath said Denning would be remanded in custody until his trial.