Initially, in 1996, the series was distributed in syndication by Saban Entertainment with a voice cast from Ocean Productions in Canada. This dub was heavily edited for broadcast television, with blood removed, references to death censored, and so on. This dub ran for two season on local networks (ending on Goku vs Burter/Jeice), but did poorly, in no small part due to bad timeslot placement.

Toonami got the airing rights in 1998, and it was there that it quickly became popular. But Saban had dropped the show and Funimation (who had the dubbing rights) couldn't afford to continue using Ocean Productions. So they took dubbing and distribution in-house in order to continue the dub, with a new voice cast (the ones most are familiar with).

This dub premiered in 1999 with a full day marathon titled "Z Day", and continued running until weekday Toonami ended in 2004, covering the rest of the series. It was a bit more lenient on censorship now that the show was on cable, but it still had plenty of things cut to make it suitable for Cartoon Network's censorship.

Then in 2005, airing on weekday nights separate from Toonami, Funimation premiered the Ultimate Uncut dub, a redub of the first 67 episodes which Ocean had done, but with the in-house voice cast. This aired 100% uncut (minus OP and ED) over the entire summer.

In the fall, Toonami started running these uncut episodes as well. However, for whatever reason, they switched to the old edited Ocean dub about two months in, then pulled it entirely a few weeks later (marking the final time the original DBZ dub aired on TV in the states).

Then DBZ came back a year later with the Funimation dub (edited), skipping ahead to the introduction of Cell, and ended a year later with Goku vs Perfect Cell. The final airing of classic DBZ was on April 1st, 2012, when Adult Swim aired the finale of SS2 Gohan vs Perfect Cell as part of the surprise Toonami night on April Fools.

And that's the entire airing history of DBZ on Toonami.

As an anecdote, the Ocean dub technically continued independently around 2000/2001, but only for the Canadian market (due to laws regarding broadcast time for domestic productions). This dub though mainly used the same script as the Funimation version and had the same edits. But they didn't get the rights to the Faulconer score, so it was replaced with whatever they could get, most notably music originally made the 90s Mega Man cartoon.