Lee, who has led the children and young people’s cancer charity for the past four years, will take up her new role in April.
She will succeed Jeremy Hughes, who announced in September that he would step down in the next year once a replacement was found. He has been in the role since 2010 and will step down shortly after Lee joins.
The Alzheimer’s Society said Lee’s proudest moments at Clic Sargent included successfully lobbying the government to fund the funerals of all children under the age of 18, founding the Children and Young People with Cancer Coalition and winning a £15m partnership with the supermarket chain Morrisons.
The society said her mother was diagnosed with vascular dementia in 2006 and until recently had lived independently with support from the charity and others.
An Alzheimer’s Society spokesman declined to reveal how much Lee would be paid to lead the charity.
The charity’s latest annual report, for the year to the end of March this year, shows that its highest-paid employee, who is not identified, received between £150,000 and £160,000 over the course of the year.
In a statement, Lee said she was privileged to have the opportunity to lead the charity.
"Having had first-hand experience of the devastation that a dementia diagnosis can have on a family, along with the amazing professionalism, warmth and understanding the Alzheimer’s Society team of committed volunteers and staff bring to that heartbreak, growing the impact of this organisation is truly a dream job for me," she said.
Hughes said he was proud to be passing the reins to Lee. "Having worked with her before, I can think of no one better to lead the Alzheimer’s Society’s determination to make life better for people affected by dementia, today and tomorrow."