Lauri Love, 31, has been charged with hacking into US government systems.
He has Asperger's Syndrome and faces a 99-year-prison sentence.
Love, who also suffers from depression and severe eczema, has said a jail term in the US would cause his health to deteriorate and would lead to a mental breakdown or suicide.
He has faced a three year battle to avoid extradition to the USA.
He is alleged to have stolen huge amounts of data from US agencies including the Federal Reserve, the US Army, the Department of Defence, Nasa and the FBI, in a spate of online attacks in 2012 and 2013.
His parents have warned that they fear he will not survive the prison system.
Speak to Premier earlier in the year Rev Alexander Love said: "What worries us most is that my son has stated emphatically that he will kill himself if he gets extradited to America.
"He just couldn't countenance being away from his mum and dad, we are like his carers - we look after him."
He went on: "I'll be honest with you, we come home some days and we think he might have killed himself. We live with this and we are scared at times.
"When your first baby is born you go and check they are breathing while they are asleep in the cot, you just want to make sure. We are worried about what might happen to him.
"And he has on more than one occasion sat there scratching away said to us 'mum, dad if it wasn't for you I would kill myself'. If he gets taken to America, he won't have that support."
One hundred and five MPs have signed the letter including Christians David Burrowes and Sir Gerald Howarth.
The letter details "significant concern that Mr Love's physical and mental well-being would deteriorate and become unmanageable if extradited."
They are asking for him to be prosecuted for any crimes he is accused of in the UK where his mental well-being can be better managed.
US authorities have been fighting for Mr Love, who lives with his parents near Newmarket in Suffolk, to face trial over charges of cyber-hacking, which his lawyers say could mean a sentence of up to 99 years in prison if he is found guilty.