The wrongful-death civil complaint was filed Saturday at a federal court in Washington, D.C., by the Center for Justice & Accountability on behalf of Colvin's sister and niece. It seeks compensatory and punitive damages.
Relatives say that Colvin was "assassinated by Syrian government agents" in the 2012 rocket strike, in what they called a premeditated and targeted attack "to silence local and international media as part of its effort to crush political opposition."
"The rocket attack was the object of a conspiracy formed by senior members of the regime of Syrian President Bashar al-Assad," the documents say.
They claim that Colvin, 56, and other journalists were tracked and that broadcast signals had been intercepted by the Syrian military intelligence department "to determine the location of the Media Center."
The journalists had set up a makeshift media center in the Baba Amr neighborhood in the city of Homs, where they reported on the suffering of civilians in the city besieged by the military.
The documents say that on or around February 4, 2012, Syrian military and intelligence forces launched a campaign against the neighborhood with systematic artillery and sniper fire.
"As part of the siege of Baba Amr, the Assad regime hunted down journalists and media activists who sought to expose these atrocities to the world," the documents say.
French journalist Remi Ochlik also died in the strike, while British photographer Paul Conroy, Syrian activist Wael al-Omar and French journalist Edith Bouvier were injured.
The documents claim that throughout February 2012, "the Assad regime received tips from intelligence sources in Lebanon that Colvin and other foreign journalists were traveling to Syria through Lebanon and reporting from the Baba Amr Media Center."
"Acting on these tips, senior members of the Assad regime formed a plan to intercept the journalists' communications, track their movement to locate the Media Center, and kill the journalists with artillery fire," they say, adding that the plan "was formulated at the highest levels of the Syrian government."
Throughout the civil war, the Syrian regime has denied targeting innocent civilians -- though it has referred to members of the opposition as "terrorists."
Colvin's relatives claim that there were "no lawful military targets," such as armed rebels, in the vicinity of the media center.
The strike occurred before rebel groups such as Al Nusra and ISIS gained a strong presence in the city, the documents say.
The San Francisco-based Center for Justice & Accountability claims the lawsuit is the first of its kind, seeking to hold the Assad regime responsible for war crimes.
"Marie Colvin was killed for exposing the Assad regime's slaughter of innocent civilians to the world," said Scott Gilmore, the attorney who led the investigation.
"The regime wanted to wage a war without witness against the democratic opposition. To do that, they needed to neutralize the media."
Colvin's sisten, Cathleen Colvin, one of the plaintiffs, said the case was "about carrying on Marie's work."
"We are seeking truth and justice not just for her, but for thousands of innocent Syrians tortured or killed under the Assad dictatorship. We hope our case will clear a path to bring those responsible to justice."
Colvin was a celebrated war correspondent who reported for The Sunday Times in Britain. She lost her left eye after it was hit with shrapnel during her coverage of the Sri Lankan conflict in 2001, forcing her to wear an eye patch, which became something of a trademark for her and a symbol of her fearlessness.
Just hours before her death, she gave one of her final interviews to CNN's Anderson Cooper, in which she spoke of her anger and fear when faced with the shelling of civilians in the city.
She said It was "a complete and utter lie that they're only going after terrorists" in the interview.
"The Syrian Army is simply shelling a city of cold, starving civilians," she said.
She also spoke of the heartbreak at watching a baby hit by shrapnel die in a poorly-equipped makeshift medical center.
"The baby's death was just heartbreaking," she said in the interview. "We just watched this little boy, his little tummy, heaving and heaving as he tried to breathe. It was horrific. My heart broke."
Colvin, a Yale graduate renowned for reporting on war's more human consequences, had for years worked in conflict zones and high-risk areas.