None of these solutions worked for me on OS X El Capitan 10.11.6. Probably because OS X has a native version of openssl that it believes is superior, and as such, does not like tampering.
So, I took the high road and started fresh...
cd /usr/local/src
If you're getting "No such file or directory", make it:
cd /usr/local && mkdir src && cd src
Download openssl:
curl --remote-name https://www.openssl.org/source/openssl-1.0.2h.tar.gz
Extract and cd in:
tar -xzvf openssl-1.0.2h.tar.gz
cd openssl-1.0.2h
Compile and install:
./configure darwin64-x86_64-cc --prefix=/usr/local/openssl-1.0.2h shared
make depend
make
make install
Now symlink OS X's openssl to your new and updated openssl:
ln -s /usr/local/openssl-1.0.2h/bin/openssl /usr/local/bin/openssl
Close terminal, open a new session, and verify OS X is using your new openssl:
openssl version -a