The Brotherhood said in a statement that Amin died at the age of 81 after falling ill.
Amin had left Cairo to London two months before the army ousted elected President Mohamed Morsi in mid-2013 following massive protests against his administration.
Egyptian authorities have launched a massive crackdown on supporters of Morsi and his embattled Muslim Brotherhood group, detaining thousands and killing hundreds.
In December of 2013, the military-backed authorities declared the Brotherhood a "terrorist" group following a spate of attacks against security facilities.
The authorities accuse the Brotherhood of condoning violence, a claim dismissed by the group, which says it is committed to peaceful activism.