I've belatedly just looked at the existing LEO entries and seen 'make a volte-face,' which is also close (though fairly elevated diction, possibly even worth marking [formal]). Drawing on that you could also consider 'do an about-face,' or perhaps even 'flip-flop' (v.) [informal]. However, all those often have the slightly negative connotation of inconsistency, unpredictability, changing one's mind; that doesn't fit ideally with the Acts story, but it may be okay with the metaphor in modern German.
A more positive related idea: 'turn over a new leaf.'
One listing of idioms has 'vom Saulus zum Paulus wandeln' instead of 'werden':http://www.redensarten-index.de/suche.php4?su...
'See the light' is more toward sudden realization (arriving at an endpoint) than drastic reversal (making a 180-degree turn). I'm not sure it translates back the other way very reliably, or at least, it would be good to include some other translations too:
see the light (fig.: undergo conversion) - das Licht schauen (geh.)
I saw the light (I realized my error etc.) - mir ging ein Licht auf (ugs.)
he'll eventually see the light (he'll realize the truth) - ihm werden die Augen noch aufgehen
finally I saw the light (inf) - endlich ging mir ein Licht auf (inf); (morally) endlich wurden mir die Augen geöffnet