You can easily install the desired NVIDIA software on Ubuntu. If you build TensorFlow from source, you have to manually install the above-listed software requirements. Consider using a TensorFlow image (Docker -devel) as the base, because this will make it easier to consistently deploy Ubuntu with all the required software dependencies.
It should look like this:
export LD_LIBRARY_PATH=$LD_LIBRARY_PATH:/usr/local/cuda/extras/CUPTI/lib64