Via Starwars.com:

THE EMPIRE’S ULTIMATE WEAPON WAS THOUGHT TO BE TRULY DESTROYED. IT WASN’T.
One of the prized pieces in my collection is the original Death Star model from Star Wars: A New Hope. Although I’ve been extremely lucky and fortunate to pick up many great items over the years, the one and only Death Star model used in filming A New Hope stands out as my number one conversation piece, dominating tours of our home and frequently a topic in many interviews (including prior StarWars.com and Star Wars Insider stories). The Death Star was almost lost for all time, but through a series of coincidences and foresight by some dedicated people along the way, it survives to this day.

The story begins in south California in 1977 where many of the props and models used for Star Wars were kept in a facility called Dollar Moving and Storage. The storage unit was rented by the studio and upon completion of postproduction, the studio decided they no longer wanted to pay rent and ordered everything in storage to be discarded. One of the employees working there at the time, Doug W., recalled that some items were retrieved by the crew prior to ending their lease, but the rest of the items were slated to be thrown away. Doug and other employees at the facility placed the majority of the items into dumpsters. For novelty sake, Doug saved a few pieces from going into the trash and kept the Death Star model and two larger surface pieces from the Death Star trench sequence.

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