The United Nations Security Council authorised countries on Friday to "take all necessary measures" to fight the jihadist group, in a resolution a week after the Paris attacks that claimed 130 lives.
Cameron called the vote on the French-drafted text an "important moment".
"The world has united against ISIL (Islamic State). The international community has come together and has resolved to defeat this evil, which threatens people of every country and every religion," he said in a statement.
"The UN Security Council has unanimously backed action against this evil death cult in both Syria and Iraq.... Today's vote shows beyond doubt the breadth of international support for doing more in Syria and for decisive action to eradicate ISIL."
Britain is taking part in airstrikes on Islamic State targets in Iraq and the government intends to seek parliamentary approval to extend these to Syria -- if it can secure a consensus across parties.
However, Jeremy Corbyn, the pacifist leader of the main opposition Labour Party, is against any such action.
In 2013, Cameron's government suffered a scarring defeat in parliament over its plan to join international military action over the use of chemical weapons by Syrian President Bashar al-Assad.
"Britain will continue to support our allies who are fighting ISIL in Syria," Cameron said.
"I will continue to make the case for us to do more and to build support in parliament for the action that I believe is necessary for Britain to take to protect our own security, as part of a determined international strategy.
"We cannot expect others to shoulder the burdens and the risks of protecting this country."