Trace levels of mercury in a natural gas are removed in a gas processing plant in an amine unit and/or a dehydrator. The mercury removal occurs concurrently with the removal of acid gases in an amine unit, e.g., an absorber or scrubber, with an amine solution containing a complexing agent. The mercury removal can also be carried out concurrently with the removal of water in a glycol dehydrator with the addition of a complexing agent to the glycol solution. Volatile mercury in the natural gas is removed by the complexing agent, forming non-volatile mercury species in the rich amine/glycol solution.