The singer told the crowd about his medical condition as he finished his set at British Summer Time Hyde Park.
He said he had found a donor and would perform three more shows before the operation in September, saying: "I'm all good, I'm all good."
Fans greeted the news with a loud, supportive cheer, applauding the 69-year-old singer as he left the stage.
He had just finished playing the song Superstition when he told the crowd he wanted to prevent "rumours" spreading about his health.
"I'm all good, I'm all good, all good, I have a donor and it's all good," he said.
"I want you to know, I came here to give you my love and thank you for your love. I love you and God bless you."
The NHS says the most common reason for needing a transplant is kidney failure or end-stage chronic kidney disease.
It is possible to donate a kidney while still alive as people only need one kidney to survive.
Wonder's support act at Saturday's gig was his friend Lionel Richie.
In 2017 Wonder paid tribute to the former Commodores front man by covering Easy at his Kennedy Centre Honours ceremony.
Richie later remarked: "I got into the business because I wanted to be like Stevie Wonder, so for all of a sudden for Stevie to be singing my song, it was surreal."