Crisis said that Sparkes would join the charity in the autumn from Unicef UK, where he has been chief operating officer for the past two years.
Sparkes, who was chief executive of Scope for almost six years until November 2009, will take over from Leslie Morphy, who announced in January that she would leave the charity in the summer after almost eight years in charge.
A spokeswoman for the charity, which had an income of £22.2m in the year to the end of June 2013, was unable to confirm before publication how much Sparkes would be paid.
Steve Holliday, chair of Crisis, said Sparkes had an impressive track record and he was looking forward to working with him.
Sparkes said it would be a privilege to lead Crisis. "I am delighted to be joining Crisis – it’s an amazing organisation providing essential services to help homeless people rebuild their lives," he said. "The charity has ambitious plans for the future, particularly in campaigning to tackle the root causes of homelessness."