Mysql - How to convert date from ISO 8601 format and save to mysql column?

You can use the STR_TO_DATE function:

UPDATE table1 SET col2 = STR_TO_DATE(col1,'%Y-%m-%dT%TZ')

Example:

mysql> select STR_TO_DATE('2013-09-05T10:10:02Z','%Y-%m-%dT%TZ');
+----------------------------------------------------+
| STR_TO_DATE('2013-09-05T10:10:02Z','%Y-%m-%dT%TZ') |
+----------------------------------------------------+
| 2013-09-05 10:10:02                                |
+----------------------------------------------------+
1 row in set (0.00 sec)

If you want to take care of the timezone just use this query, and use the mysql timezone

mysql> select CONVERT_TZ("2013-09-05T10:10:02Z", "+00:00", @@session.time_zone);

+-------------------------------------------------------------------+
| CONVERT_TZ("2013-09-05T10:10:02Z", "+00:00", @@session.time_zone) |
+-------------------------------------------------------------------+
| 2013-09-05 12:10:02                                               |
+-------------------------------------------------------------------+
1 row in set, 1 warning (0.00 sec)

or any other timezone

mysql> select CONVERT_TZ("2013-09-05T10:10:02Z", "+00:00", "+03:00");
+--------------------------------------------------------+
| CONVERT_TZ("2013-09-05T10:10:02Z", "+00:00", "+03:00") |
+--------------------------------------------------------+
| 2013-09-05 13:10:02                                    |
+--------------------------------------------------------+
1 row in set, 1 warning (0.00 sec)

You can also use CAST('2013-09-05T10:10:02Z' AS DATETIME) which does not require a format definition as in STR_TO_DATE().