Normalize many-to-many data

Question

I have a non-normalized database that establishes a many-to-many relationship this way.

Article table:

| id  | category_ids | some_more_columns |
| --- | ------------ | ----------------- |
| 1   | []           |                   |
| 2   | [1, 2]       |                   |
| 3   | [3]          |                   |

Category table:

| id  | some_more_columns |
| --- | ----------------- |
| 1   |                   |
| 2   |                   |
| 3   |                   |

I want to make a proper many-to-many relationship like:

Article table:

| id  | some_more_columns |
| --- | ----------------- |
| 1   |                   |
| 2   |                   |
| 3   |                   |

Category table:

| id  | some_more_columns |
| --- | ----------------- |
| 1   |                   |
| 2   |                   |
| 3   |                   |

Finally, Article has categories table:

| id  | article_id | category_id |
| --- | ---------- | ----------- |
| 1   | 2          | 1           |
| 2   | 2          | 2           |
| 3   | 3          | 3           |

I want to write a script to populate the table of Article_has_categories using the column of category_ids in the Article table in MySQL. I'm very young in SQL, so this is very overwhelming. Please shine some light!