The 34-year-old New Zealander, who held the WBO title from 2016 to 2018, had denied taking a prohibited substance but risked a two-year ban.
He failed the voluntary test on the day he fought and lost to Britain's Fabio Wardley. British media reported at the time that he had tested positive for traces of cocaine.
"I'm pleased to confirm my provisional suspension is lifted and I'll be back in the ring soon," Parker said in a statement.
"I've been advised to say no more for now while details are finalised. Thank you to all my supporters."
Robert Smith, general secretary of the British Boxing Board of Control, confirmed the suspension had been lifted but gave no details.