Lisa King, who was born in Haddington but now lives in Florida, went under the knife on Christmas Eve and remains in intensive care in Duke University Hospital, North Carolina.
A series of life-threatening infections delayed her surgery by weeks, with husband Jon fearing that she might not even make it to the operating table
But world-leading surgeon Dr Allan Friedman has cut out a “significant part” of the tumour, which he described as “like a small potato in size”.
And doctors expect her to make rapid progress over the next two to six weeks despite some weakness and speech problems caused by the surgery.
Devoted Jon, 53, who has waited anxiously at her bedside, described his relief now that the surgery appears to have been a success.
He said: “It went as well as we could have hoped. Recovery will be a slow, steady progress but things are going well.
“Considering the trauma her head and brain have been through, I’m pretty amazed that she’s doing as well as she is.
“Dr Freidman described the tumour as being like a small potato in size, about two inches in diameter.
“Her scar reaches six inches from her forehead to the crown then turns right about 90 degrees and about another six inches down to behind her left ear.
“I’m very happy with where we are at the moment and looking forward to Lisa being well and healthy again.”
The surgery has caused significant weakening of the right arm, with Lisa’s right leg also weakened but recovering more quickly.
But Dr Freidman has insisted this was good news because it meant the maximum amount of the tumour had been removed without causing any significant damage.
However, there are some issues with low blood pressure which need to stabilise before Lisa can be moved to a standard hospital room.
So far there is no indication of a time frame for discharge and Lisa has a long recovery battle in front of her.
Born Lisa Elliot, she moved from East Lothian to America to join Jon two years ago after they met when he was a commercial airline pilot and she was an air hostess.
Soon their idyllic life in the Sunshine State was capped off with the best news possible – their first child was on the way after two years of trying.
But within months of learning they were due to be parents Lisa lost their baby after just 11 weeks – and that was only the beginning of their nightmare.
Soon after the miscarriage, Lisa, faced a string of painful life-threatening infections, before being diagnosed in September with an aggressive brain tumour that was initially feared to be inoperable due to its ferocity, depth and size.
Unwilling to give up on his wife, Jon sought a second opinion and transferred Lisa more than 600 miles from the Holmes Regional Hospital near their home in Melbourne, Florida, to the Duke University Hospital in North Carolina.
There they consulted Dr Friedman – who operated on former Massachusetts senator Ted Kennedy in 2008, a year before his death.