Avni Metra, 53, came to Britain in 1998, one year after he killed two brothers in his native Albania.
He was convicted in his absence of both murders and possession of firearms, Westminster Magistrates' Court heard.
District judge Margot Coleman told Metra, who had argued he would not get a fair trial abroad, his life in Britain was "based on a lie".
Metra, who was living in Borehamwood, Hertfordshire, was arrested by Scotland Yard detectives on 8 June as he drove through Watford, after a tip-off from the Daily Mail.
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He told an earlier extradition hearing: "There is no justice in Albania. There is only corruption."
The labourer, who claimed he had originally fled to Britain because his life was in danger after a friend was killed, also argued that he had a right to a private and personal life.
But Judge Coleman said: "You called absolutely no evidence to support your assertion that you would be denied the right to a fair trial.
"There are no grounds that have been heard before me to reach that conclusion.
"As far as your family are concerned, you were convicted of assaulting [your wife] and subjected to a restraining order."
Metra is also barred from seeing his children without permission, the court heard.
The case will be sent to the Home Secretary, who will make the formal decision on whether he should be extradited, and Metra will remain in police custody, the court was told.

The 50km (31 mile) HK Ultramarathon saw competitors cover the same stretch of road 25 times.
Nestor Wong won the event in 3:24:20 and defended the course, saying it helped to hear the cheering crowds.
An ultramarathon is defined as any race above the standard marathon distance.
Ahead of the event, local runners criticised the course.
"It will be boring and very difficult, if not dizzy, for the runners who will have to do 25 laps of the same stretch of road," Thomas Kiprotich told the South China Morning Post.
"I don't mind monotonous courses, but this is a bit extreme monotony for my tastes," Michelle Lowry added.
Kwan Kee, chairman of the Hong Kong Amateur Athletic Association and one of the race organisers, conceded that the course was "quite boring".
But he told AFP spectator access would help: "It was great that we could secure this course in the heart of the city... land in Hong Kong is very limited."

The England Lions batsman ended on 117 as the hosts made 255-6 in 92 overs in their pursuit of overhauling Kent for second spot and £43,000 prize money.
Skipper Daryl Mitchell weighed in with 67 as he completed 1,000 first-class runs for the fourth time in his career.
Ben Cotton picked up 3-46for Derbyshire on his firstteam recall.
The visitors have not managed a Championship away victory and are hoping to avoid going an entire season without a win on the road for the first time since 2008.
Worcestershire batsman Joe Clarke told BBC Hereford & Worcester:
"It was quite difficult out there. The pitch is very slow. Once you get in, it is a lot easier but to start with it is very tough.
"It has got a little bit more pace in it now but this morning it was very slow and credit to Daryl Mitchell. He did a fantastic job in getting us through that period.
"It meant a lot to get a hundred because we've been struggling a little bit with the bat.  In the last few weeks, we haven't been getting the scores we'd have liked and to be there at the end is very pleasing.
Derbyshire bowler Ben Cotton told BBC Radio Derby:
"It was nice to take a couple of wickets on my return. It took me a while to settle in for the first five or six overs, then I found a nice rhythm and took the wickets we needed.
"You've just got to put as many balls as you can in the right area and hopefully there is enough there to take an edge or get an lbw.
"Tony Palladino and Tom Milnes started well after tea and put some pressure on them and due to their hard work I took a wicket and managed to get another near the end as well."
A double murderer who posed as a refugee to enter the UK illegally is to be extradited.
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Hundreds of runners have competed in Hong Kong's first inner-city ultramarathon, despite organisers describing it as "quite boring".
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Joe Clarke made his fifth County Championship century of the summer as Worcestershire batted out the opening day against Derbyshire at New Road.