The cause of death is unknown, but Cattermole was found in his home on Maundy Thursday and pronounced dead later that day.
"It is with great sadness that we announce the sudden passing of our beloved son and brother Paul Cattermole," the group and Cattermole's family said in a joint statement.
The police do not suspect that any crime has been committed.
As recently as February, S Club 7 announced a comeback tour on the occasion of the 25th anniversary of the group's formation.
"Grateful for all the memories""
On their social media, the group's members write that they "lack words to describe the deep sadness and loss we all feel" and that they are "grateful for all the incredible memories we shared".
S Club 7 was formed by Simon Fuller, the man behind the Spice Girls, in 1998 and during its five active years had a string of hits such as "Don't stop movin'", "Reach" and "S Club party".
Sang on the Queen's 50th birthday
The group's track record includes four British number-one hits and a Buckingham Palace performance at Queen Elizabeth's celebration of 50 years on the throne in 2002.
The planned reunion had been the band's second, after a brief comeback in the mid-2010s. The plan for this year's reunion was to give about ten arena concerts around the UK and Ireland.