Alsina, who joined Bowel Cancer UK in 2008 as director of services and strategy before becoming chief executive a year later, led the charity through its merger with Beating Bowel Cancer, which was completed last year.
She was named Charity Chief Executive of the Year at the Third Sector Awards in 2017 and was awarded an MBE in 2016 for services to bowel cancer patients.
Alsina, who lost her father to bowel cancer in 2007, said working for Bowel Cancer UK had been "the greatest privilege of my professional life to date".
She said: "I have had the great joy of working with an incredible group of committed staff, trustees, volunteers, leading clinicians, scientists and policy-makers, and a wonderful community of people affected by bowel cancer whose selfless determination to drive positive change for others has inspired and motivated me every day."
She said one of the greatest challenges faced by any charity chief executive was knowing when it was time to leave.
"So although my commitment to saving lives from bowel cancer is undiminished, it is with a huge mixture of emotions that I have decided to leave my role at Bowel Cancer UK."
Alsina said she had a "strong commitment to tackling ageism within our society and to ensuring everyone has the opportunity to live a happy, independent and fulfilling older life".
Patrick Figgis, chair of Bowel Cancer UK, said the charity was "indebted to Deborah for the outstanding leadership she has provided".
He said: "Helping bring together two bowel cancer charities has one has been one of her greatest achievements in her constant pursuit to enhance outcomes for people affected by the disease.
"She has championed national policy change, provided endless support to patients and their families and has rightly been recognised for her service to bowel cancer patients."
Justine Frain, chair of Independent Age, said Alsina had a keen understanding of the issues affecting older people and would be a "passionate advocate" for the charity.