Pastor Hassan Abduelraheem Kodi and Czech aid work Petr Jasek were arrested after they raised money to help a man injured in a protest.
State officials claim they are spies and a court sentenced the pastor to 12 years behind bars whilst Jasek was given a 23 year stretch.
They were both given substantial fines.
Lawyers will now announce their intention to appeal within the next few days.
It comes after the UK Government said it was deeply concerned" about their convictions.
A third man, campaigner Abdulmonem Abdumawlla, was also sentenced to 10 years in prison for espionage and inciting hatred crimes.
