In the NZR statement Williams, a practising Muslim, clarified his preference was to avoid wearing logos from banks, alcohol brands and gambling sponsors on his team uniform.
"I want to be clear that this is nothing personal against the BNZ or Investec," he said. "My objection to wearing clothing that markets banks, alcohol and gambling companies is central to my religious beliefs and it is important to me to have been granted this exemption.
"As I learn more and develop a deeper understanding of my faith, I am no longer comfortable doing things I used to do. So while a logo on a jersey might seem like a small thing to some people, it is important to me that I do the right thing with regards to my faith and hope that people respect that.
"I know I'm not perfect. Every day I work hard to become a better person. I want to thank the Blues and New Zealand Rugby for working with me through this matter over the last couple of days and respecting my religion and accommodating my request."
NZR general manager of rugby Neil Sorensen said Williams' stand would be respected and thanked the affected sponsors for their understanding.
"Sonny holds clear religious beliefs in relation to this matter and we respect those," Sorensen said. "Conscientious objections need to be genuine, and we believe this is."