"I've been doing something, at the end of the show, every night, and it's been dedicated to my brother Liam Payne"
The 40th anniversary version contains vocals from late artists including David Bowie, George Michael and Liam Payne
Payne's funeral took place earlier this week
The pair previously feuded at the 2013 BRIT Awards
Payne's girlfriend Kate Cassidy, Cheryl's Girls Aloud bandmates and James Corden also joined the late singer's family at the service
Upon news of Payne’s death, Williams recalled how the “trials and tribulations” the One Direction star faced were very similar to his own
The One Direction singer died on October 16 at the age of 31
"He had the biggest heart, he was always the first person to offer help in any way that he could"
A press release stated that in the 72-hour period prior to his death, Payne had traces of "alcohol, cocaine and prescription antidepressants" in his body