The 55-year-old was taken to the Borders General Hospital at Melrose for treatment and later transferred to the Edinburgh Royal Infirmary, but medics were unable to save his life, and he died in the early hours of today, March 22.
His name has not yet been released by police, but they have confirmed that he was from Edinburgh.
The accident that claimed his life took place between Selkirk and the Kingsknowes roundabout, west of Tweedbank, at around 12.20pm on Tuesday, March 20.
His red Kawaskai ZZR 600cc bike left the road as he was travelling northbound past Boleside.
Sergeant Andy Gibb, of Police Scotland’s Lothians and Borders road policing unit, said: “Our condolences are with the family and friends of the man at this sad time.
“We’d ask anyone who may have information which can assist with our ongoing inquiries to contact Police Scotland on 101, quoting incident number 1,382 of March 20.”
The road was closed for over three hours after the accident to allow specialist police officers to carry out an investigation to try to establish how it happened.