The High Court heard that Richard O'Dwyer, from Sheffield, has signed a "deferred prosecution" agreement with US authorities.
Law enforcers in the US claimed that the 24-year-old's TVShack website had hosted web links to pirated movies and TV shows.
After a court ruling in May, Home Secretary Theresa May approved the Sheffield Hallam student's extradition to the US, where he could have faced prison if convicted over the allegations.
But O'Dwyer will instead travel to America voluntarily in the next 14 days for his deal to be formally ratified, reports BBC News.
It is understood that he will pay a "small sum" in compensation and give undertakings to the US authorities that he will not infringe copyright laws again.
Following this, he will return to the High Court to have his extradition application formally dropped.
Judge Sir John Thomas said that it was a "very satisfactory outcome", and expressed his hope that the matter would be "resolved happily before Christmas".
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The US Immigration and Customs Enforcement agency brought the case against O'Dwyer and TVShack.net after claiming that the site earned more than $230,000 (£147,000) in advertising revenue by offering copyrighted material.
The domain name was seized by US authorities in June 2010, and then shut down.
After O'Dwyer's extradition order was agreed by the Home Secretary in May, Wikipedia founder Jimmy Wales hit out at the decision, saying that it was the US trying to "prosecute a UK citizen for an alleged crime which took place on UK soil".
Human rights campaign group Liberty has welcomed O'Dwyer's proposed "deferred prosecution" deal, but said that it shows extradition laws are in need of urgent reform.
"This will be a huge relief for Richard, but how appalling that he had to wait so long for the US authorities to make this decision," said Isabella Sankey, Liberty's director of policy.
"Case after case shows that our extradition arrangements must be overhauled to allow people who have never left these shores to be dealt with here at home."