Mapp was forced to resign last after being voted out by the ABS and the Amateur Boxing Association of England (ABAE).
UK Sport threatened to redirect more than £10.4 million of its funding set aside for the BABA for the Rio 2016 Olympics into an alternative Special Purpose Vehicle, after expressing concerns at the way Mapp was removed.
Following positive talks, a deal has now been reached which means the BABA will continue to receive funding.
"We are very happy with the outcome and look forward to the on-going success of the World Class Performance Programme (WCPP) and creating opportunities for the best young boxers produced by England, Scotland and Wales to progress their talent and win medals on the international stage," said Thomas.
"We welcome the additional funding from the WCPP for talent pathways which will strengthen the link between elite boxing and grass roots activity."
UK Sport continues to look for an independent chair who has not been affiliated with the ABAE, ABS or the Welsh Amateur Boxing Association (WABA) for the last four years.
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- Sports & Recreation
- Amateur Boxing Association