get the CUDA and CUDNN version on windows with Anaconda installe

Use the following command to check CUDA installation by Conda:

conda list cudatoolkit

And the following command to check CUDNN version installed by conda:

conda list cudnn

If you want to install/update CUDA and CUDNN through CONDA, please use the following commands:

conda install -c anaconda cudatoolkit
conda install -c anaconda cudnn

Alternatively you can use following commands to check CUDA installation:

nvidia-smi

OR

nvcc --version

You could also run conda list from the anaconda command line:

conda list cudnn

# packages in environment at C:\Anaconda2:
#
# Name                    Version                   Build  Channel
cudnn                     6.0                           0

Although not a public documented API, you can currently access it like this:

from tensorflow.python.platform import build_info as tf_build_info
print(tf_build_info.cuda_version_number)
# 9.0 in v1.10.0
print(tf_build_info.cudnn_version_number)
# 7 in v1.10.0

As of TensorFlow 2.4.1, We can use tensorflow.python.platform.build_info to get information on which CUDA, cuDNN the binary was built against.

>>> import tensorflow
>>> print(tensorflow.__version__)
'2.4.1'
>>> import tensorflow.python.platform.build_info as build
>>> print(build.build_info)
OrderedDict([('cpu_compiler', '/usr/bin/gcc-5'), ('cuda_compute_capabilities', ['sm_35', 'sm_50', 'sm_60', 'sm_70', 'sm_75', 'compute_80']), ('cuda_version', '11.0'), ('cudnn_version', '8'), ('is_cuda_build', True), ('is_rocm_build', False)])

The build.build_info is an OrderedDict. So to get CuDNN and CUDA versions:

>>> print(build.build_info['cuda_version'])
11.0
>>> print(build.build_info['cudnn_version'])
8

Note: As this is not a public API, things can change in future versions. In previous versions, we could do from tensorflow.python.platform import build_info as tf_build_info; print(tf_build_info.cuda_version_number) like in jdehesa's answer.