When you install Exchange 2013, you’ll notice that the console you’d expect to see has been dropped in favour of a web-based management console. This can be found here:

https://yourexchange2013server/ecp

This URL isn’t presented in the start menu/modern UI or particularly obvious after the installation. If you’re setting up a greenfield environment the URL above should get you straight to the new Exchange 2013 Admin Center.

I don’t see the 2013 Exchange Admin Center when I browse to ECP, I get redirected to the old Exchange 2010 ECP page

Exchange 2010 ECP
Exchange 2010 ECP

There is a caveat if you are coexisting with Exchange 2010, if this is the case you will have to specify the Exchange version in the URL to get to the Exchange 2013 Admin Center:

https://yourexchange2013server/ecp/?ExchClientVer=15

Exchange 2013 Admin Center
Exchange 2013 Admin console