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, pleaded guilty to 26 counts of indecent assault on a male person and three of indecency with a child.
The charges he denies are two offences of buggery, one of attempted buggery, eight of indecent assault on a male person and one of indecency with a child.
Wearing spectacles and a grey fleece, he entered the 41 pleas with a clear voice.
Denning, of Basildon in Essex, was one of the original Radio 1 line-up when the station was launched in 1967.
He was also the first announcer heard on BBC2 when the television channel took to the air in 1964.
He was first arrested by detectives from sex crime inquiry Operation Yewtree in June last year.
Judge Alistair McCreath told him he would be remanded in custody until his trial, which is expected to last up to two weeks.