Prosper of Aquitaine was a contemporary, so I'll let him tell it:
""In the year 406, the Vandals and Alans, having crossed the Rhine,
entered Gaul on the day before the kalends of January..."
A few years ago, Michael Kulikowski published a paper which made a good argument that the invasion actually began on 12/31/405, but in recognition of the long acknowledged 406 date (and because I wasn't blogging about stuff like this last year), I'll call today the anniversary. Happy Barbarians Day!
* For want of an approved term