The film, starring Mark Ruffalo, Michael Keaton and Rachel McAdams, has already landed the top prize at the Screen Actors Guild Awards and is nominated for six statuettes at the Oscars, to be held on February 28.
Singer paid tribute to abuse survivor Phil Saviano as he picked up the trophy at the Los Angeles ceremony hosted by American stand-up comedian, writer and actor Patton Oswald.
“He’d been trying to tell his story for a very long time and I think that story is finally now being told a needs to continue to be told,” Singer said.
“Spotlight,” beat out “Bridge of Spies,” “Sicario,” “Straight Outta Compton” and “Trainwreck,” written by its star Amy Schumer.
Charles Randolph and Adam McKay scooped the prize for best adapted screenplay for their work transforming the book “The Big Short” into the film of the same name.
The movie, set on the eve of the 2008 global financial meltdown, bested highly-touted rivals, including “Carol,” “The Martian,” “Steve Jobs” and “Trumbo”.
It is nominated for five Oscars, including nods for best director for McKay and best supporting actor for Christian Bale.
“Millions of people lost their homes, millions of people lost their savings, and that’s really what this was about,” said McKay.
“And in the end we just want people to really look at why these banks had taken control of our government.”
Best documentary screenplay went to Alex Gibney for “Going Clear: Scientology and the Prison of Belief,” a condensed history of the church and its founder, L Ron Hubbard.
In the television category, “Mad Men” won best TV drama, “Veep” took best TV comedy series and “Mr Robot” scooped best new TV series.
The WGA awards is one of the last major award ceremonies ahead of the Oscars.