Using pathauto, it should be quiet easy with a pattern like :

news/[node:{NAME_OF_TAXONOMY_FIELD}:entity:name]/[node:title]

With hierarchy :

news/[node:{NAME_OF_TAXONOMY_FIELD}:entity:parents:join-path]/[node:{NAME_OF_TAXONOMY_FIELD}:entity:name]/[node:title]

gl

Using pathauto, it should be quiet easy with a pattern like :

Normal way :

news/[node:{NAME_OF_TAXONOMY_FIELD}:entity:name]/[node:title]

With hierarchy :

news/[node:{NAME_OF_TAXONOMY_FIELD}:entity:parents:join-path]/[node:{NAME_OF_TAXONOMY_FIELD}:entity:name]/[node:title]

In your case, this should work

[node:{NAME_OF_TAXONOMY_FIELD}:entity:url]/[node:title]