Otti was a prime instigator in the LRA joining peace talks that began last year in Juba, South Sudan.
Rumours of his death had been circulating for weeks in Uganda, with various rebel and mediator sources saying he had been arrested by Kony.
A peace process mediator said Kony had punished Otti on allegations of spying while Ugandan media have said there was a dispute over money and control.
Otto said problems arose because Otti was promoting peace.
"The rift between Vincent and Kony is because Otti wanted peace talks and Kony was completely against," he said.
Otto said Kony informed him about it via phone from the LRA's hideouts in the eastern Democratic Republic of Congo (DRC).
"Then Kony later called me and my colleague, Odong Richard, justifying Otti's execution," he said.
The seven LRA deserters, who included four commanders and three child combatants, surrendered themselves this week to the UN peace mission, Monuc, in Congo.