The low-cost carrier has said it will introduce a five-times-weekly service from Edinburgh to the Bavarian capital on 31 March.
A year-round, twice-weekly service to Germany's third largest city will also start on the same date from Glasgow.
Eurowings' parent company Lufthansa currently operates a seasonal Saturday flight from Glasgow to Munich.
Edinburgh Airport's chief executive Gordon Dewar said the announcement came as the airport was on course to have handled in excess of 12 million passengers by the end of the year.
Mr Dewar said: "I am delighted that Edinburgh Airport has a direct new service into Bavaria; this offers even greater choice and is further confirmation of Edinburgh Airport's position as a leader for connectivity between Scotland and the continent for both business and leisure passengers.
"We are well on course to have handled in excess of 12 million passengers by the end of the year and we are continuing to grow, create jobs and make a positive contribution for Scotland's economy."
Munich was Edinburgh's first twin city in 1954 and this new link reinforces and renews business and cultural ties between Bavaria and Scotland.
Gavin Barrie, City of Edinburgh Council's economy convener, said: "This is fantastic news for Edinburgh. As well as being a great boost to the city's economy, the new airline will further strengthen our existing links with Munich, the first international city to be twinned with Edinburgh in 1954.
"The airport plays an important part in increasing visitor numbers to Edinburgh and the new airline will benefit business links as well."
Francois Bourienne, commercial director at Glasgow Airport, said: "We have enjoyed real success in strengthening our connectivity with key European cities, all of which have generated significant demand from passengers.
"This introduction of Eurowings' direct service to Munich is fantastic news for Glasgow and for our passengers.
"Not only will it result in a regular twice weekly service to one of the wealthiest regions in Europe, our passengers will have access to the extensive onward connectivity offered by the Lufthansa network."
German airline Eurowings is to launch direct flights to Munich from Scotland's two busiest airports.