This is the canon hand-wave explanation:
http://starwars.wikia.com/wiki/Old_Republic
The Galactic Republic in its current form existed for 1000 years but there was an older Republic that existed for many years before that. The Jedi preceded the Galactic Republic and protected the Old Republic as well. The birth of the Galactic Repblic seems to coincide closely with the relative disappearance of the Sith.

EDIT: I think this sounds good

Episode I
THE PHANTOM MENACE

For almost a thousand years the
knights of the Jedi Order have
protected the Galactic Republic
Now, after a millennia of peace,
dark forces conspire in the shadows
of the galaxy.

Attempting the seize the
Abundant resources of the
Planet Naboo, the nefarious
TRADE FEDERATION has
surrounded the planet with a
blockade of deadly warships.

With the newly crowned Queen
desperate for help, the Supreme
Chancellor has secretly
dispatched two Jedi Knights to
settle the conflict.

I would like to add something that mentions that the Chancellor is sort of in a tenuous place and is fearing the crisis blowing up could be the final straw that ends his political career, but there’s only so much space.

EDIT: Thanks for the offer Hal, but I think I’m going to create the crawl myself. I’m going to use the Star Wars TSG program for Mac.