Tyson Fury has set his sights on a title fight with Anthony Joshua after being cleared to box again following a deal with UK Anti-Doping. Fury, along with his cousin and fellow heavyweight Hughie, have accepted a backdated two-year doping ban for testing positive for elevated levels of nandrolone in February 2015. However a separate charge against Tyson Fury for refusing to take a drug test in September 2016, which could have carried a four-year ban, has been withdrawn.

Both men continue to deny any wrongdoing – and say the high levels of nandrolone came from the ingestion of offal, uncastrated wild boar or contaminated supplements. Tyson Fury, who has not fought since winning the world heavyweight crown against Wladimir Klitschko in November 2015, responded to the news by immediately tweeting Joshua, who holds the WBA, IBF and IBO world titles: “Where you at boy? I’m coming for you punk. No one blocking my path now!”

Fury then jokingly suggested he may appear on the bill of his friend, the British middleweight Billy-Joe Saunders, when he defends his world middleweight title in Canada on Saturday. In a statement Fury, 29, 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.

“Hughie and I have maintained our innocence from day one and we’re now happy that it has finally been settled with Ukad and that we can move forward knowing that we’ll not be labelled drug cheats. I can now put the nightmare of the last two years behind me and next year I will be back doing what I do best, better than ever and ready to reclaim the world titles which are rightfully mine.”

The Ukad chief executive, Nicole Sapstead, said there was “absolutely no whitewash and nothing to be fearful or embarrassed about” in the decision. However, she confirmed her organisation would launch an internal review to learn any lessons from what she called “an exceptional case”.

Sapstead also accepted Ukad had made a mistake by not telling the Furys they could be charged when they were first interviewed after failing a doping test – and that it had taken too long to charge the fighters after their positive tests in February 2015.

Sapstead explained the delay was because her organisation had needed to seek additional scientific research into nandrolone and consult the World Anti-Doping Agency and an expert in nandrolone.

“The Furys argued they were in some way legally prejudiced because of delay,” she added. “It was probably a failure on our part. In hindsight and when we run a review of this case, that will probably be something that emerges out of it. But we’re not in the business here of just frivolously charging athletes and hoping a charge will stick.”

Sapstead also conceded the failure to keep Furys informed was “intrinsically linked” to Tyson Fury’s refusal to take a test last year. However, she denied the spiralling legal costs of the case had been a factor in the surprise compromise decision.

“We have thrown an unprecedented amount of resources at this,” she said. “Yes, one of the elements does have to be the money side of things. But that was not to sole reason we got to where we got to – absolutely not. We would’ve fought this to the nth degree.”

Under the compromise, Hughie Fury’s victory against Andriy Rudenko on 21 February 2015 along with Tyson’s win over Christian Hammer a week later are disqualified – and any and all titles, prize money and ranking points are forfeited.

However, Ukad accepted that because both fighters were not put on notice of their alleged anti-doping violation until June 2016, and had not committed any doping offences after February 2015, the results they obtained in their fights after that date should not be disqualified. Crucially it means Tyson Fury’s shock victory over Klitschko remains in the record books.

The case was also complicated by several factors, including Tyson Fury failing a test for cocaine use in September 2016 and later admitting using the recreational drug to deal with depression related to his injury and Ukad problems.

However, Monday’s decision allows both parties to claim a partial victory. As Sapstead admitted: “It isn’t as if you’re going to go: ‘This is a brilliant outcome.’ A compromise is a compromise.”