The German carrier will end a 20-year spell in which Glasgow has had no direct flights to the city with six flights a week from April 8, increasing to a daily frequency from June 24.
The move follows several years in which international airlines have concentrated growth at Edinburgh, establishing it as Scotland's busiest airport, with over two million more passengers a year than Glasgow.
The announcement prompted a jubilant reaction by business leaders, tourism groups and the leader of Glasgow City Council, Gordon Matheson, who said there had been a concerted effort to lure the airline.
A spokesman for Edinburgh Airport expressed disappointment, saying it would work hard to convince Lufthansa and other airlines of the benefits of flying to the capital. Lufthansa said it would maintain its Edinburgh to Frankfurt service.
The transfer has been decided six months after Glasgow Airport's owner BAA was forced to sell Edinburgh to comply with a ruling by the Competition Commission designed to increase competition in the central belt.
Lufthansa, which launched its Edinburgh-Dusseldorf service two years ago, said the move had been driven by passenger demand. The service is thought to be heavily used by German business passengers travelling more to the west of Scotland than the capital.
Amanda McMillan, managing director of Glasgow Airport, said: "The introduction of the Dusseldorf service is fantastic news for Glasgow Airport as not only will it result in a direct, daily flight to one of the wealthiest regions in Europe, our passengers will once again have access to the extensive onward connectivity offered by the Lufthansa network."
A spokesman for Edinburgh Airport said: "We can't understand the commercial logic behind this move and firmly believe that retaining the route at Edinburgh would have better served Scottish passengers.
"We'll work hard to convince Lufthansa and all of the airlines serving Scotland that Edinburgh offers significantly more value than any other airport."