The American chart-topper told fans of his condition as he wrapped up his set at British Summer Time in London’s Hyde Park.
He told the crowd he had a donor and that he will perform a few more shows before he takes a break ahead of the procedure planned for September.
Wonder, 69, said: “I’m all good, I’m all good, all good, I have a donor and it’s all good.
“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 news was greeted by cheers of support from fans, who gave him a raucous applause as he was led off stage.
According to the NHS, kidney failure or end-stage chronic kidney disease is the most common reason for needing a kidney transplant.
Unlike many other types of organ donation, it is possible to donate a kidney while still alive as people only need one kidney to survive.
Although there is no upper age limit, very few places will perform a transplant on patients over the age of 70 unless they are very fit, according to Kidney Care UK.
Wonder’s appearance at BST saw him headline the Hyde Park event in the second of five major concerts at the London park.
He had the crowd cheering as he treated them to classics like For Once in My Life, and Master Blaster.
Wonder stopped repeatedly between tracks to thank fans for their support over the years.
Those gathered to watch the multi Grammy Award-winner were treated to the crooner tinkling the ivories as he performed tracks like Signed, Sealed, Delivered.
His show, called The Song Party, was supported by Lionel Richie – who warmed up the crowd – on the Great Oak Stage on Saturday.
In December 2017, Wonder performed a cover of Easy at Richie’s Kennedy Centre Honours ceremony, which left Richie visibly emotional.
He later said: “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.”
His set also featured a tribute to musicians who have died, including songs by Michael Jackson, Amy Winehouse, Prince and Aretha Franklin.
Like Celine Dion the previous night, Wonder, who has amassed worldwide sales of more than 100 million units, sang John Lennon’s Imagine.
Wonder, who has received more than two-dozen Grammy Awards, has produced a string of hits over a long career that began when he was a youngster who performed as Little Stevie Wonder. His classic hits include You Are the Sunshine of My Life and Living for the City.
His fans revelled in the warm summer night – though a light drizzle fell near the end – and the career-spanning retrospective that evoked Wonder’s early days as a young Motown star.