It appears to be a combination of the Lucasfilm Story Group and the individual fimmakers; a Slashfilm article, which I believe was based on the LSG live panel from Celebration Anaheim 2015, says:
The first point made at the panel was that the Story Group has a long game plan. They have major beats and ideas spanning probably years or maybe decades in advance (Note: no specific time frame was given) so as to be able to incorporate everything Star Wars is becoming.
While the term “Story Group” may make it sound like they are dictating the story, that’s not usually the case. In most cases, authors or filmmakers who are hired to work on Star Wars properties, are given the oppurtunity [sic] to come up with their own stories and ideas. While doing that, they work closely with the Story Group to make sure the stories are authentically Star Wars (for example, Darth Vader doesn’t dance or something) and also fit into the larger plan. Hidalgo said they’ve heard pitches from people who have great ideas for characters who are then told, “Come back in six years.” That’s because the story they’re pitching would fit in better with a character at another point in the future.
Although the LSG has a long-term plan for how the Star Wars universe will unfold, the fine details are left in the hands of the individual fimmmakers (in close consultation with the LSG, to keep the canon consistent).
The most visible members of the Lucasfilm Story Group, and the ones you'll mostly hear giving answers to questions, are:
- Kathleen Kennedy, President of LucasFilm
- Pablo Hidalgo, currently a creative executive with the LSG
- Leland Chee, who before the Great Disneyfication had the thankless task of maintaining the Holocron, Star Wars' internal continuity database