Brighton enjoyed Europa League wins over Ajax, Marseille and AEK Athens this season to top their group before being knocked out in the last 16 by Roma.
They are 10th in the Premier League before their final game on Sunday and can finish no higher in the table.
“I am sure our fans will give Roberto and his staff a wonderful and fully deserved send off at the Amex before, during and after tomorrow’s match,” Bloom added.
“In the meantime, I’d like to thank Roberto and his staff for all their hard work in the past two seasons. They all leave our club on good terms and with our very best wishes for the future.”
De Zerbi was appointed after Graham Potter left for Chelsea and Brighton have since sold the likes of Leandro Trossard, Alexis Mac Allister, Robert Sanchez and Moises Caicedo for a combined total of more than £200m.
“We have agreed to end my time at Brighton so that the club and I can continue to work in the way that suits each of us best, following our own ideas and visions, as well as our work and human values,” said De Zerbi.
“Leaving now provides me with time to take a break before deciding on my future plans.
“I am very sad to be leaving Brighton, but I am very proud of what my players and staff have achieved with the support of everyone at the club and our amazing fans in the past two historical seasons.”
Seven members of De Zerbi’s coaching staff will also leave but first-team coach Andrew Crofts and goalkeeper coach Stern will remain with the club.