The mandate, which requires parliamentary approval, includes reconnaissance jets, refuelling aircraft, a frigate to protect a French aircraft carrier and up to 1,200 military personnel to the region for a year.
Germany's lower house of parliament is set to debate the issue and a vote is expected later in the week.
German Chancellor Angela Merkel's cabinet has approved plans to help France and other nations fight self-proclaimed Islamic State militants in Syria.
It follows an appeal from French President Francois Hollande for an escalation of the international military effort against IS following the November 13 attacks in Paris, which killed 130 people.
German Foreign Minister Frank-Walter Steinmeier says the decision is a sign of his country's solidarity with France.
"We have decided to put into practice the solidarity which we promised France and that is the reason for this morning's decision of the German cabinet to become engaged, together beside France, in the military conflict with IS and al-Nusra and related groups in Syria."
A defence ministry spokesman says two planes could be sent to Turkey's Incirlik air base next week, provided the plans are approved by the parliament.
Mr Steinmeier says it's still important to work towards a political solution for Syria.
"All of this cannot however distract from the point that we still believe that the war in Syria, at the end of day, will not be solved with military means but we are still pushing for a political process which was bravely started just a few weeks ago in Vienna and which after two rounds agreed a road map for the future path."
Germany, which is already arming Iraqi Kurds fighting IS, will not join France, the United States and Russia in conducting air strikes in Syria.
But its contribution is significant given the country's post-World War Two history of avoiding foreign military entanglements and voter misgivings about getting involved in the conflict.
Meanwhile in Britain, Prime Minister David Cameron says his nation must stand with its allies in confronting extremism.
"It's about the politics and the diplomacy and the humanitarian aid, all of which we need to bring to bear to bring peace to Syria but to make sure we protect our interest, our national interest, fighting against this appalling terrorist organisation."
US Defence Secretary Ash Carter says the United States is expanding its special operations force in Iraq to help Iraqi and Kurdish forces fight IS militants.
"We're at war. We're using the might of the finest fighting force the world has ever known. Tens of thousands of US personnel are operating in the broader Middle East region. More are on the way. We have some of our most advanced air and naval forces attacking ISIL."
Mr Carter also notes the specialised US expeditionary force in Iraq will be positioned to carry out unilateral operations against IS in Syria.
But he says its primary focus is defending Iraq's borders and building the capacity of the Iraqi government forces.
"Through our own action and those of our coalition partners, the military campaign will destroy ISIL's leadership and forces, deprive it of resources and safe haven and mobility. All the while we seek to identify and then enable motivated local forces on the ground to expel ISIL from its territory, hold and govern it, and ensure that victory sticks."
