The new GDAL 2.1 is now also packaged for Fedora 23 and 24 which is possible due to the tireless efforts of various Fedora packagers.

Repo: https://copr.fedorainfracloud.org/coprs/neteler/GDAL/

Installation Instructions:

su

# Fedora 23+24:
# install this extra repo
dnf copr enable neteler/GDAL

# A) in case of update, simply
dnf update

# B) in case of new installation (gdal-devel is optional)
dnf install gdal gdal-python gdal-devel