You cannot prove that the binary you provide really matches a given source code. It is not theoretically impossible but it would require substantial cooperation on the part of the compiler. Some researchers are working on that subject for some languages which are better suited to that task than C (mostly ML or Lisp derivative). In any case, there is no readily available product yet, and won't be for some time, so in practice, that's not an option.
Your best options are then:
- Provide the source code (with proof that it is the same archive as the one used by the independent reviewer) so that the users may do the compilation themselves.
- Ask the people who ran the "independent review" to actually do the compilation and provide the resulting binary.
In any case, users will have to trust someone: you, the independent reviewers... in as much the same way as they have to trust Microsoft, Intel, AMD and all other parties involved in the building of the computer. So maybe the question is not the right one. The compiler itself may push a backdoor on clean source code (there is a very classic example of that kind of trick). Instead of asking how you could prove that the compilation step did not include a backdoor, you should ask: how may I build enough of a good reputation so that people will trust me ?