Air Carrier Captain reported a fume event during cruise. Flight crew completed depressurization procedures which dissipated smoke and the flight continued to destination.

Narrative

On Date at approximately XA:34 enroute from ZZZ1 to ZZZ we received a smoke baggage fire master caution warning at 35;000 ft. on the C track between ZZZZZ and ZZZZZ1 intersection. Smoke began to fill the cockpit and cabin. We determined the cause to be environmental and no fire was detected in the baggage area. We tried to isolate and clear the cabin using the smoke removal procedures but were unsuccessful. We then advised ATC; off set 2miles right of course (slop) and started a descent to 10;000 ft. where we could start the depress procedure to clear the cabin of smoke. In the descent to 10;000 ft. we established communication with ZZZ2 radio; squawked and via CPDLC with ZZZ3. After reaching 10;000 ft. we were able to shut down the environmental system and clear the cabin of smoke. The crew and passengers were on supplemental oxygen during the descent until level off at 10;000 ft. We were able to proceed direct to ZZZ. With no further action. We reestablished communication with ZZZl Center and advised them we were no longer an emergency aircraft and requested priority for landing in ZZZ. We then requested direct ZZZ airport. There were two crew; and two passengers onboard. No injuries or significant damage discovered. We were able to land safely in ZZZ with no emergency services required. I was asked to call upon arrival and gave a statement to ZZZ Center/FAA/FSDO.