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Which sentence is correct? 

  • my project is dependent upon your project completing
  • my project is dependent on your project completing.
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Well it all depends..................... – user75318 May 15 '14 at 20:28

They are equivalent; upon is just a more formal term for on, and it is especially used in abstract senses.

The NOAD reports the following note about the usage of upon:

The preposition upon has the same core meaning as the preposition on. Upon is sometimes more formal than on, however, and is preferred in the phrases once upon a time and upon my word, and in uses such as row upon row of seats and Christmas is almost upon us.

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protected by tchrist Mar 1 '15 at 18:18

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