Professor Pier Paolo Mariani examined Totti and gave the go-ahead for an operation using keyhole surgery.
"More than the reconstruction of the ligament, in truth it was a substitution, as it was replaced with part of the patella tendon," explained the medic.
"The recovery time should be around four months and we hope to see him back on the field then. Now he will do physiotherapy for a month, then work with fitness coaches."
It is better news than expected, suggesting the Roma captain could be playing again for the start of the season in September.
Professor Mariani also performed the operation when Totti fractured his ankle just over two years ago.
"At the time it was a shock and he went straight from the field to the operating theatre.
"Now he has had 24 hours to absorb the impact of what has happened, but he has the right desire to come back better than ever – just as he said."