In southeastern Europe, an area covering Bulgaria, Croatia, Cyprus, Greece, Romania, Serbia and Slovenia, the rise will be 9.2 percent, while Western Europe will see a rise of 2.7 percent.
Only Italy, Greece and Sweden will keep budgets stable, although Sweden is planning hikes after 2016.
Slovakia, for example, is buying nine UH-60 Black Hawk multirole helicopters to replace Soviet-designed M-17 helicopters.
"Even if the Russian threat recedes, the trend will remain up due to terrorism, accentuated by the lack of commitment by the US in the Middle East," he added.
The German defense budget is due to rise by 6.2 percent between 2015 and 2019, the report said.
The think tanks point to a growth in defense pacts among European countries, in response to the Russian threat, which are spurring spending, including the Swedish-Finnish Naval Task Group.
At the NATO defense ministers' meeting in Brussels in June last year, Bulgaria, Croatia, Hungary and Slovenia signed to cooperate on special forces aerial capabilities, meaning training, modernization, procurement and potentially even integrated multinational units.
Various small European countries are strengthening ties with Germany and the US, including a Polish-German deal to develop an amphibious wheeled Armoured Personnel Carrier. In Western Europe, Germany and France are teaming on a new battle tank, while France and UK work on a new UAV.
The trend appears to mark a change from the traditional vicious circle in Europe by which few joint programs meant little cross border industrial integration, which in turn did little to encourage joint programs.
"We are now seeing a lot of industrial cooperation, particularly at Tier 2 and 3 in the supply chain," said John Louth, a senior research fellow at the RUSI think tank in the UK, which contributed to the report.
"I link that to a rise in joint programs, while even national programs are using a larger number of international suppliers, thanks to the use of rare materials or very high tech," he added.
Apart from the direct reaction to Russian foreign policy or terrorism, European countries are also hiking defense spending in response to appeals from NATO and the US, said Louth.
"It looks like bilateral relations with the US do count. If you are in Talinin, having a few thousand US troops is important," he said.
Italy stands out as the European country which does not appear to be hiking spending in 2016, a result of tightened budgets.
Details of that cash will be made available in a secondary budget document to be released this spring, which will also give a breakdown on spending per program.
The current document made it clear however that various programs will not be launched, including the arming of Italy's UAVs, permission for which has been granted by the US after a long wait.
But John Louth predicted Italy would soon be spending more. "If you look at the crisis in the Mediterranean and the Italy White Paper on defense, it seems they will have no choice but to spend more in the future," he said.