Sudan is accused of providing economic support, places for the suicide bombers to train and false documents.
The judge is still to decide on the amount of compensation
Experts testified that Sudan had given safe haven to Osama bin Laden's al-Qaeda terrorist network since 1991 – long before Yemeni operatives blasted a 12m hole in the side of the USS Cole in Yemen's port of Aden on October 12, 2000.
Lawyers representing the Sudanese government declined to comment after Wednesday's ruling.
Doumar said that he would issue a written opinion later to fully explain his ruling.
Shalala Swenchonis-Wood, whose brother died in the attack, said on Wednesday: "Words can't express the loss my family has gone through.
"It's not financial, it's not material, it's always the things, the little things you don't see."
"It would not have been as easy - it might have been possible - but it would not have been as easy"
R. James Woolsey, former CIA director
The families want $105m in damages, but potential damages could be reduced to $35m.
The judge, however, has said he is inclined to apply the 'Death on the High Seas Act', which permits compensation for economic losses but not for pain and suffering.
Four experts on terrorism, including R. James Woolsey, CIA director from 1993 to 1995, also testified to support the families' position that al-Qaeda needed the African nation's help to carry out the attack.
"It would not have been as easy - it might have been possible - but it would not have been as easy,'' Woolsey said in a videotaped statement.
The experts cited testimony from other trials, a declassified Canadian intelligence report, US state department reports and their own studies as they testified that Sudan let terrorist training camps operate within its borders.
They also accused Sudan of giving al-Qaeda members diplomatic passports so they could travel without scrutiny and diplomatic pouches to ship explosives and weapons without being searched.
The US has listed Sudan as a state sponsor of terrorism since 1993.