Three packages containing the substance were recovered from the Piper Bravo platform on Saturday.
The discovery prompted the large-scale drug screening of all staff on board amid concern it could have been an illegal substance.
But analysis carried out by Police Scotland has now revealed that the packages simply contained crushed medication.
A force spokesman said: "Police Scotland can confirm that testing on packages found on the Piper Bravo platform has now been completed.
"Testing has established that the packages did not contain illegal substances but crushed medication which is commonly used for pain relief."