The radical cleric and four other British nationals can be extradited to the US, the European Court of Human Rights ruled.
Human rights judges said that the radical preacher and four other British nationals can be extradited to the US.
Richard O'Dwyer, 23, could face up to 10 years in a federal prison after Home Secretary Theresa May approved his extradition.
A cross-party group of MPs are to launch a bid to tighten up extradition rules in the Commons.
Conservative MP Dominic Raab said he was attempting to amend the Anti-social Behaviour, Crime and Policing Bill to stop British citizens being the victims of miscarriages of justice in foreign courts.
Almost 30 MPs have supported the amendments including Labour's Keith Vaz and Gisela Stuart.
If the bill is agreed after a debate in the Commons on Tuesday, the amendments would effect both the European Arrest Warrant (EAW) and the UK-US extradition treaty.
The amendments proposed would strengthen the checks needed for a British citizen before extradition can take place under the EAW.
The decision on whether a suspected ally of hate preacher Abu Hamza should be kicked out of Britain will be made by human rights judges today.
Currently being held at high-security psychiatric hospital Broadmoor, Haroon Aswat, is wanted by US prosecutors for allegedly plotting with Hamza to set up a terror-training camp in Bly, Oregon.
Aswat's case was adjourned to allow judges more time to consider his mental health as he is currently being treated for schizophrenia.
Student Richard O'Dwyer said he is looking forward to returning to normality after striking a deal with US authorities over his TVShack website.
"I'm happy it's finally over," he told the BBC. "I still maintain I never thought I was committing a crime.
"I'm glad the US has decided to drop the case. It's a pity the UK wasn't able to resolve this."
He added: "I'm looking forward to getting back to university and see all my friends."
- Richard O'Dwyer could have faced jail if convicted of the allegations.
- The allegations were brought following a crackdown by the US Immigration and Customs Enforcement agency.
- The agency claimed the TVShack.net website earned more than $230,000 (£147,000) in advertising revenue.
- US authorities obtained a warrant and seized the domain name in June 2010.
- It is thought Mr O'Dwyer will return to the UK with his family today.
Earlier this year Home Secretary Theresa May approved Mr O'Dwyer's extradition, which he appealed.
– Richard O'Dwyer's mother Julia O'Dwyer
The UK government was happy to allow Richard's extradition to proceed, just like they have with others similarly accused of conduct in Britain, committed without ever setting foot in the US.
The Government is using a rotten law which was designed to bring fugitive offenders back to the place where a crime was committed, not for outsourcing our criminal justice system to another jurisdiction.
I feel very sorry for those people and their families who have not been as lucky as ours and who are still suffering under this rotten extradition law.
Richard O'Dwyer's deal with the US is "a first" in extradition cases, his lawyer has said.
Under the agreement, O'Dwyer must pay US authorities £20,000 and not break any US laws, "associate only with law abiding people" and work regularly in a lawful occupation.
– Mr O'Dwyer's lawyer, Ben Cooper
So far as we know this is a first in extradition cases - and a sensible solution for UK defendants faced with an ever-growing extra-territorial reach of US prosecutions.
I expect this mechanism will be used by UK defendants in future US extradition cases now the precedent has been established and at least until the Government introduces the promised forum amendment into the Extradition Act 2003.
– Mr O'Dwyer's lawyer, Ben Cooper
Richard O'Dwyer is very happy to put this behind him. He has avoided extradition and will avoid a conviction.
The solution reached is pragmatic and allows Richard to finish his final year at university and get on with his studies at a crucial time in his life. We are grateful that the US recognised it was in everyone's interests to find a practical solution.
A student who ran a website where users could stream pirated films has "avoided a conviction" after paying £20,000 to US authorities, his lawyer has said.
Richard O'Dwyer, from Sheffield, ran the TVShack website hosting links to pirated films and TV programmes.
But after a court hearing in New York, the 24-year-old avoided extradition and conviction by signing a Deferred Prosecution Agreement.
As a result he paid £20,000 to the authorities, representing the profits he made from TVShack between December 2007 and November 2009.
The money will be distributed among victims whose copyrights were infringed by TVShack.
The law is already on the statute book but needs to be activated. However, since the forum ban cannot be used retrospectively, it will not apply to Gary's case.