McKinnon's appeal will be heard in a two-hour session in the House of Lords. He will be represented by his solicitor, Karen Todner, a specialist in extradition law.
The former systems administrator says he spent two years hacking into a number of US government systems looking for evidence of extraterrestrial life. He is accused of illegally accessing computers belonging to the US army, navy, air force, NASA, the Department of Defense as well as a number of private companies.
Among his hacking tools was a Perl script which tied together projects from other people.
US prosecutors have acted angrily to McKinnon's actions. McKinnon says that US authorities offered him a plea bargain with a sentence of 3-4 years, but that they were not prepared to guarantee that figure. He says that US representatives then pursued the maximum sentence available, and said he would be "turned over to New Jersey authorities to see him fry".
The maximum sentence is likely to be life imprisonment.
His case on Monday is based around the way in which the plea bargaining process was carried out.
McKinnon told SCMagazine today: "It was very threatening behaviour. I'm being treated as some kind of terrorist".
McKinnon denies deliberately causing any damage but he said: "I absolutely regret doing it".
The US government claims McKinnon caused $700,000 worth of damage.
If McKinnon loses the appeal, he says he will use his final chance of an appeal at the European Court of Human Rights, and have the extradition put on hold.
If he wins the appeal, he says the extradition will be thrown out. He could then still face charges through the UK justice system and it would be unlikely he could ever leave the country for fear of further action.
If the Lords dispute what was said during the plea bargaining process, the case could be referred back to Bow Street Magistrates Court, where the case was heard earlier.
The case will be heard by five lawlords including Lord Phillips of Worth Matravers, the third most senior judge in England and Wales behind the Lord Chancellor and the Lord Chief Justice.
Their decision is likely to be presented in three to four weeks.
McKinnon told SCMagazine that he had some hopes of success. "My chances are the best they've ever been," he said.
McKinnon said that if he wins, he hopes it will set a precedent for extraditions to the US and says he will "spend a lot of time" trying to get the Extradition Treaty changed.
Under the terms of the treaty, which came into being in 2003, the US government has not had to show any evidence of McKinnon's hacking or any damage it might have done, in order to request his extradition.
McKinnon was arrested in 2002. The extradition order was signed by then Home Secretary John Reid in 2006.
During his hacking attempts, he claims that he succeeded in finding evidence of extra-terrestrial life in the form of images and spreadsheets.
"I saw photos in space of things that didn't look man-made," McKinnon said. "And I saw an Excel spreadsheet with non-terrestrial officers with their names and ranks. That makes me think there's a space force being developed in secret".