Laura Plummer, 33, was arrested as she flew into the Red Sea resort of Hurghada last October.
The shop worker from Hull was carrying 290 Tramadol tablets in her suitcase.
The very strong painkillers are legal in the UK and are available by prescription, but are banned in Egypt.
Ms Plummer said she was carrying the tablets for her partner Omar Caboo who, she said, suffers from severe back pain.
On Boxing Day Ms Plummer was sentenced to three years in prison by a Cairo judge.
But according to The Sun newspaper Ms Plummer is set to be released imminently.
The report says that Egypt's President Abdel Fattah el Sisi has pardoned Ms Plummer as part of the country's Revolution Day celebrations.
The paper reports that Ms Plummer's brother and sister have flown to Egypt to bring her home.
Sister Jayne Synclair told The Sun: "We can't believe it's over. We've prayed for this day since she was arrested. We just want to get her home. "
Ms Plummer is reported to have told her family in an emotional phone call: "I never thought this day would come. I'd given up hope."
The Foreign and Commonwealth Office said: "We continue to provide assistance to Laura and her family and our embassy remains in regular contact with the Egyptian authorities."