The consortium - a partnership between the German government and industrial giants Siemens and ThyssenKrupp AG - has declined to say how much the deal is worth.
Transrapid said the magnetic monorail link will be built by the end of 2003, and will allow passengers to travel at an average speed of 430km/h (270mph) between Shanghai's airport and the city centre.
The 30km (19 mile) journey should take less than 10 minutes.
There has been no official confirmation of the deal from the Chinese authorities, although Beijing and Berlin had agreed last year to carry out a feasibility study for such a project.
If the Shanghai deal is confirmed, it will be the first commercial application of the Transrapid rail system, which has struggled to win contracts because of its high cost.
Billion-dollar deal
In a statement, Transrapid said the agreement had been reached with Prime Minister Zhu Rongji and Shanghai Mayor Xu Kungdi. The contract is expected to be signed on Monday.
The consortium - a partnership between the German government and industrial giants Siemens and ThyssenKrupp AG - has declined to say how much the deal is worth.
But it follows an initial feasibility study agreed last year, which itself cost more than $730,000. Some estimates say the deal could be worth billions.
As a sweetener, Germany is reported to have offered China loans and grants of nearly $500m to help finance the project.
Magnetic levitation
The Transrapid rail link is based on the Maglev system, which uses powerful magnets to hold a train a few millimetres from the track, and propel it with little noise and vibration.
Germany has poured billions of dollars into developing the technology, but last year it scrapped a plan to build a rail link between Berlin and Hamburg after eight years of planning and development.
Berlin is said to be considering other shorter stretches for the high-speed train.
Transrapid said it hopes the Shanghai deal will boost other projects in the United States as well as China, were a 1,300km link between Shanghai and Beijing is said to be under consideration.