A mega fight between the two has always been mooted, especially as Joshua was the one who pieced together the fragmented heavyweight championships after Fury lost the belts by being stripped of his titles and then retiring.
Fury's license was revoked by the BBBofC in October 2016 and his cousin Hughie Fury, 23, was also cleared after he too tested positive in 2015.
Former unified heavyweight world champion Fury is keen to rebuild his career and reputation following his positive test for elevated levels of nandrolone in February 2015, which he and his cousin Hughie blamed on eating an uncastrated boar.
Both men contend that they "never knowingly or deliberately committed a violation".
It means the "Gypsy King" just has to regain his boxing licence from the British Boxing Board of Control (BBBofC) - who have accepted the outcome - to resume fighting again.
A separate charge against Tyson Fury for refusing to take a drug test in September 2016 was withdrawn by UKAD.
The message is addressed to Matchroom promoter Eddie Hearn, who promotes British rival and current undisputed heavyweight champion Anthony Joshua.
Fury said: "I'm a fighting man through and through and I've never backed down from anyone in my life and I was certainly not going to back down from fighting this dispute".
He now claims to be on the road to full fitness and has spoken of his desire to reclaim the world titles, which are "rightfully" his.
"Tyson Fury's boxing licence suspension will be considered by the stewards of the board in January", the board said on Wednesday.
A BBBofC statement said: "The British Boxing Board of Control acknowledges United Kingdom Anti-Doping's decision in relation to Tyson and Hughie Fury. I'm coming for you punk [isn't] no1 blocking my path now!"
Both fighters' respective bouts in February 2015, including Tyson's victory over Christian Hammer, have been disqualified but results after that date, including the win over Klitschko, stand. Hughie was out-pointed by New Zealand's Joseph Parker on Sep. 23.
WBC heavyweight champion Deontay Wilder says he would welcome Tyson Fury back to the ring and would want to fight him - once the Briton is fit enough.