The 25-year-old was taken to hospital after the British middleweight title contest was stopped in round 10.
Blackwell woke from the induced coma on Saturday, and by Sunday was talking to family and friends at his bedside, said promoter Hennessy Sports.
Blackwell had suffered a bleed on the skull and not the brain as initially reported, the statement added.
Hennessy Sports said the boxer had won his "toughest fight yet".
It added: "Nick Blackwell won the hearts of over three million television viewers on 26 March with an astonishing display of all-action bravery and determination.
"In the past week, however, he has humbled millions more. He's a fighter. He's a warrior. He's a true champion and gentleman.
"On behalf of Nick, his family, and very close friends, we'd like to thank everyone for their continued support and well-wishes. It has been overwhelming at times and has certainly not gone unnoticed."
