Three small 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 commonly used for pain relief.
“Police enquiries have now concluded and no further action will be taken.”
A spokeswoman for platform operators Talisman Sinopec Energy UK said: “We have been working with Police Scotland following the discovery of an unknown substance on the Piper Bravo platform on Saturday.
“We have now been advised by police that the substance was crushed medication commonly used for pain relief. No illegal substances of any kind were present. Police enquiries have now been concluded.
“In line with our company procedure, all personnel on board underwent substance-testing by medics. Talisman Sinopec Energy UK continues to operate a zero tolerance approach to illegal substances.”