The specific organization that provided the final approval for the New Balance development isn't explicitly listed in the search results. However, from available context, developments like these typically require various levels of approval from city planning and development authorities.
In the case of New Balance's $500 million Boston Landing mixed-use project, it's likely that the final approval would have come from local government bodies, such as Boston's planning and development authorities. For example, the Boston Planning & Development Agency (BPDA) is typically involved in approvals for large development projects within Boston.
For the most accurate and specific information, checking official announcements from NB Development Group or the relevant city planning departments would be recommended.
Here are some relevant sources: