The 31-year-old's decision to cover up the logo was questioned by New Zealand Prime Minister Bill English on Monday.
"New Zealand Rugby and the Blues have accommodated Sonny Bill Williams' request to have advertising from the BNZ and Investec removed from his Super Rugby playing jersey," the NZR and Blues said in a joint statement.
Two-times World Cup winner Williams said he preferred not to wear 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," Williams added.
"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.
"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."
However, the ruling does not apply to the removal of Investec from the tournament logo on all Super Rugby team jerseys.
Williams has told NZR that he has no objection to sporting advertising from insurance companies but has already been dropped from promotional activities with All Blacks' sponsor AIG.
(Reporting by Shravanth Vijayakumar in Bengaluru)
