LibreSSL is a drop-in replacement for OpenSSL.
Note that recently a big clean up of the openssl codebase has taken place so openssl master no longer exposes the internals of structs etc. meaning it's both more auditable and more maintainable. This code is not yet released however.
Distributions such as CentOS/RHEL which are focused on stability are not going to replace OpenSSL in any existing releases.
I've been testing this against each release for some time and I'm very happy with it.