The defendant continues to dispute his identity, claiming he is a man called Vital Dapi from Albania.
In a statement read outside court, the Stuart family said: "To the twisted individual who committed this wicked crime: we hope you spend the rest of your miserable existence reflecting on the utter senselessness and brutality of what you did to two innocent people, and that maybe one day you will find the moral courage to tell us where Mum is so that we may give her and our family some final peace."
Qazimaj claims he had never been to the UK before his arrest and extradition from Luxembourg. He was arrested in Luxembourg on June 16, and denied murder.
During his trial at Ipswich Crown Court, it emerged that he lied to claim asylum in the UK in 1999 by saying his name was Ali Qazimaj and he was fleeing persecution in his homeland of Kosovo.
But official records in Albania uncovered during his trial confirmed that his real name was Vital Dapi who was born in Albania, rather than the former Yugoslavia.
If he had used his true identity on arriving in the UK, he would have been unable to get asylum.
Detective Chief Inspector Andy Guy, of Norfolk and Suffolk's Major Investigation Team, speaking outside court, said: "There were four key strands of evidence - the fingerprints, the DNA, the handwriting samples and the physical appearance.
"All in themselves are strong pieces of evidence and of course, put together, I think it's absolutely compelling.
"To try and argue from the witness box that you're not this man in the photograph when clearly you are is quite bizarre."
Karim Khalil QC, prosecuting, said Qazimaj had lived in Tilbury, Essex, and was a carer to the father-in-law of the Stuarts' daughter, Christy Paxman.
He said Qazimaj had gambling debts and believed the Stuarts to be millionaires. They were last seen alive on CCTV at Goodies Farm Shop in Pulham Market, Norfolk, on May 29.
A silver Citroen car was found by police in Dover and prosecutors said it had the defendant's fingerprints in it.
After the jury returned its verdicts, Judge Jeremy Stuart-Smith said: "I know you've not taken very long in absolute terms to reach your verdicts, but I don't find that at all surprising."
He said Qazimaj faced a mandatory life prison sentence.
Qazimaj will be sentenced at Ipswich Crown Court tomorrow.