How can I add a numeric version_id column to an existing table?

I have a table in a postgres db with rows versioned with a timestamp that I’d like to add a numeric version_id column to.

eg.
existing:

ID  VERSION_DATE
--  -----------------------
A   2015-02-05 21:25:56.123
A   2015-02-06 21:15:56.456
A   2015-02-07 11:25:52.789
B   2015-01-01 13:44:54.223

desired:

ID  VERSION_DATE             VERSION
--  -----------------------  -------
A   2015-02-05 21:25:56.123  1
A   2015-02-06 21:15:56.456  2
A   2015-02-07 11:25:52.789  3
B   2015-01-01 13:44:54.223  1

Is there a query that can calculate and insert the version values?