LOS ANGELES, May 7 — ABC announced on Monday that it would broadcast three more seasons of its hit castaway mystery, “Lost,” ending the show in 2010 after a run of six seasons.

The announcement has been expected since January, when the creators of the show told a group of television writers that they wanted the network to set a definitive end date for the series.

Such a date was necessary, they said, so that they could begin planning how to unravel the multiple mysteries that beset the fictional survivors of Oceanic Air Flight 815, which crashed on an uncharted island en route from Sydney, Australia, to Los Angeles in September 2004.

But the move by ABC is nevertheless unusual because networks usually try to milk profits from their successful series as long as possible, a strategy that often results in convoluted story lines, shake-ups among production staff and dwindling fan bases.

That is exactly the situation that Damon Lindelof and Carlton Cuse, two of the show’s executive producers, said early this year that they wanted to avoid. When they announced their desire to set a specific end date to the series at a January meeting of the Television Critics Association in Pasadena, Calif., they surprised even the ABC executives who were attending.

“We have always envisioned ‘Lost’ as a show with a beginning, middle and end,” Mr. Lindelof and Mr. Cuse said in a statement, which was re leased over the weekend to The Hollywood Reporter and to the rest of the news media on Monday. “By officially announcing exactly when that ending will be, the audience will now have the security of knowing that the story will play out as we’ve intended.”