The action began in 2001 under an 18th century law which allows foreigners to sue American firms in a US court.
Relatives and the union, Sintramienergetica, filed the action under the 218-year-old Alien Tort Claims Act after the slayings.
Valmore Locarno, the local union president at Drummond's open surface mine and Victor Orcasita, another union official, were pulled off a company bus and shot to death in March 2001.
Locarno's successor, Gustavo Soler, met a similar fate seven months later after also being taken off a bus.
Terry Collingsworth, the plaintiffs' lawyer, said they would appeal against the decision.
Augusto Jimenez, who headed Drummond's Colombian operations, wiped away tears after the verdict.
He declined to comment but the company said the verdict was "a long time coming".
Drummond, one of the world's largest coal-mining companies, said it will continue to co-operate in investigations into the deaths of its three employees.
"Our biggest fear right now is that union members will be left vulnerable to assassination"
Stevenson Avila, Sintramienergetica president
A paramilitary leader has been charged with Locarno and Orcasita's murders.
More than 800 union members have been killed in Colombia in the last six years, making it the world's most dangerous country for workers.
Only a few of the killings have been solved.
In Colombia, Stevenson Avila, the president of Sintramienergetica, said the ruling was likely to embolden the paramilitaries.
"Our biggest fear right now is that union members will be left vulnerable to assassination,'' he said.
Added Avila: "We knew this was becoming a question of state policy, and that America protects its companies, but we held out hope that presenting real, documented evidence of the company's responsibility, that justice would be served."