The Exodar's history is a short one, beginning with its departure from Draenor and its short journey through the Twisting Nether to Azeroth.
At some point before the present, the naaru arrived in the realm of Outland with a "dimensional fortress" known as Tempest Keep. The naaru dispersed throughout the ravaged world, leaving the fortress defenseless. Seeing an opportunity to strike, Kael'thas Sunstrider and his many blood elflegions assaulted Tempest Keep and captured it, taking possession of its treasures and kidnapping the sole naaru occupant, M'uru, sending him back to Silvermoon City for the magisters to utilize in their thirst for magic. M'uru later becomes a boss in Sunwell Plateau, transforming into the corruptEntropius.
Velen, the courageous prophet who had led the draenei people since their exodus from Argus millennia before, had hid with the remainder of his people in the wake of the Legion-instigated orcish onslaught. With the Broken Farseer Nobundo, first of the draenei shaman, at his side, the Prophet personally led a raid on Tempest Keep to wrest control of one of its satellite structures, the Exodar.
It is unknown how the draenei accomplished this, or what happened next, but the draenei took control of the Exodar and used it to escape Outland. The blood elves (and/or the draenei traitor Sironas), discovering what the draenei were planning, sabotaged the dimensional engines of the vessel. When the draenei activated it, the engine malfunctioned and sent the Exodar hurtling out of control through the Twisting Nether until it reached the closest habitable planet, Azeroth. The crippled ship screamed across the skies of Northern Kalimdor, crystals flying everywhere, until it crash-landed on a small island chain off the coast of Darkshore. The survivors took the islands as their new homeland, and set up their new capital in the largest intact portion of the still-smoking ship. The surviving blood elves regrouped and, after scouting the area, summoned reinforcements from Tempest Keep with the Sun Gate.
In the short story Prophet's Lesson, which takes place after the Shattering, The Exodar is nearly repaired. According to Vindicator Romnar, all key systems have been repaired, and they are now just cleaning up and bolstering any areas of apparent weakness. He states they should have The Exodar up and running, and operational within a week, and by the end of the short story Vindicator Maraad announces that it has been fully repaired.
After the Legion attacks the Exodar and slays O'ros, Velen orders Romuul to begin repairs and states that the draenei are going home.
The Exodar's crash caused power crystals from the Exodar to break apart from the ship and land on the island, an event the Stillpine furbolg call the "crystal storm." These crystals would then be ingested by the nearby nightstalkers causing them to become infected with corruption. Exarch Menelaous, from Azure Watch, fearing that the infection will spread if left unchecked assigns young adventures to purge the forests of infected cats.
Never seen in Nagrand, the first red elekk calves were born in Azeroth after the Exodar's arrival. Some breeders theorize that the unique coloration is somehow caused by the same radiation which ravaged Bloodmyst Isle.
The long-term effects of the contamination caused by the Exodar are still under observation.