Swift, due to perform the first of three shows in New Zealand on Friday, and Bon Jovi both performed individually at the event. The former, who sang Trouble, Love Story and 15, said she was honoured by her invite to the palace.
"This is my first time playing at Kensington Palace, or any palace for that matter," she said.
"I want to thank you for having me Prince William, this is just amazing."
Swift said it was important the gala concert was supporting at-risk youth, given they were dealing with more than most people were at what was already a difficult age.
Other guests at the event included Benedict Cumberbatch, James Blunt and Tinie Tempah.
Prince William presented the Centrepoint Great Britain Youth Inspiration Award to Bon Jovi for his humanitarian work.
The singer founded Soul Foundation in the United States in 2006, which aims to break the cycle of people falling into poverty and homelessness by helping them gain access to food and affordable housing along with job training programmes.
Bon Jovi said: "Nights like this happen once in a lifetime but the chance to affect change can last a lifetime. Each one of you tonight have that chance to affect change."
- Independent