Lisa Foster was diagnosed with stage four bowel cancer - the highest level of spread - three weeks ago.
She started raising the money so that someone can care for Ruby, Zach and baby Scarlett while she is treated.
Mrs Foster, from Derbyshire, said the nanny would also provide extra support for her husband if the worst happened.
"I just can't believe the generosity of this world and I will be forever grateful to all of those hundreds who have donated. They really have helped me," she said.
"I want to enjoy every single minute, of every single day, of every single month now of what I've got left."
Her eldest child Ruby is seven, her son Zach is four, and her baby Scarlett is seven and a half months old.
She said her biggest motivation for fighting cancer was to live long enough so that Scarlett might remember her.
She also hoped to see Scarlett's first steps or hear her first word, see Zach on his first day at school and see Ruby start secondary school.
She is recording videos for her children to watch at key milestones in their lives, such as their 18th birthdays.
Mrs Foster raised the money online through a fundraising page and exceeded her £50,000 target thanks to donations from more than a thousand people.
"A lot of people have said they feel for me because they're a similar age and they have three children," said the 36-year-old.
"If I can get a year that means I can see Zack's first day at school, I can see Scarlett maybe start walking or saying her first word, and that's what's going to keep me going."
A mother with incurable cancer has raised more than £50,000 in just six days to pay for a nanny to look after her three children.