The Aberdeen-based management consultant had a pin inserted into his spine during a seven-hour operation, soon after Sunday's fall in Florida, but he has amazed doctors at the Orlando Regional Medical Centre with the speed of his recovery.
A spokesman for the hospital said: "He has managed to take some steps and is doing very well, so well in fact that we expect him to be discharged early next week. There are no signs of paralysis and even though full rehabilitation could take three months we expect a full recovery."
Mr Griffiths, 27, has told friends how his instructor, Michael Costello, repeatedly shouted "Hey man, I'm sorry" to him as the pair hurtled towards the ground at speeds of 120 mph. Mr Costello, who saved the Briton's life by deliberately cushioning his fall, died on impact.
His funeral took place on Wednesday and his ashes are expected to be scattered from a plane. Mr Costello is set to receive a posthumous bravery award from The Royal Humane Society after being recommended by the Griffiths family.
Meanwhile, a 26-year-old women is to sue her parachute partner for negligence during a tandem skydive - the type of jump in which Mr Griffiths was hurt - which left her with horrific injuries.
Elyse Gorham is claiming damages of at least pounds 50,000 from Christopher Murphy over the accident at Headcorn airfield, Kent, in July 1993. Ms Gorham, who crashed at more than 40 mph, suffered a broken leg, ankle, pelvis and five ribs. She claims the incident has left her with deep physical and psychological scars.