The 1.3 billion Swiss francs (USD 1.32 bn) will be spread over ten years and will target lower income countries in central and eastern Europe, a statement said.
The funds are "intended to reduce economic and social disparities in Europe, which is in Switzerland's economic and political interest," it said.
Switzerland made a similar contribution to the EU over the previous decade and the extension of the programme must still be approved by parliament.
"Switzerland has shown that it is a reliable partner", Junker told reporters after the meeting.
Asked by a journalist if he had come to the wealthy Alpine nation merely to pick up a cheque, Junker countered that his purpose in Bern was not to collect "a present".
Switzerland's complex ties with the EU are sewn together through a mixture of deals on trade, labour, migration and other issues.
The Bern-Brussels relationship suffered a heavy blow in 2014 when Swiss voters backed a proposal calling for the re- introduction of migrant quotas, which could have limited the number of EU citizens working in Switzerland.
Some Swiss politicians continue to call for an updated, simpler set of agreements governing EU ties.
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