LOS ANGELES — Like the deep-sea craft James Cameron used to dive nearly seven miles down in the Pacific, the long-awaited screenplays for his three sequels to “Avatar” will soon pop to the surface, probably within weeks.

Mr. Cameron, an avid adventurer as well as one of Hollywood’s most successful directors, has been working for much of the last several years on the “Avatar” films, when he was not indulging his other passion and exploring the deepest parts of the ocean.

For those who share Mr. Cameron’s moviemaking adventures — particularly executives at 20th Century Fox, which released “Avatar” to about $2.8 billion in worldwide ticket sales almost five years ago — delivery of finished scripts will signal the beginning of perhaps their grandest enterprise.

Fox, as well as Mr. Cameron and his cohorts at Lightstorm Entertainment, his production company, are expecting the three successive “Avatar” films — set for release in three straight Decembers beginning in 2016 — to transform their companies and possibly once again to set a new standard for large-scale, multimedia entertainment.