The Blues announced on Tuesday that Lloyd will leave at the end of the AFL season, after seven years in the role.
It comes a week after Melbourne sacked Simon Goodwin. Two days after that bombshell, the Blues reaffirmed Michael Voss would stay as coach after a marathon board meeting, following a recommendation from Wright.
But with Voss confirmed, changes were also inevitable in Carlton's football department. After making the 2023 preliminary final and the top eight last season, this year they have plummeted out of final contention.
"Brad has been a central part of Carlton in recent years. He has progressed and led the football department through some significant adversity during that time, as well as back-to-back finals appearances," Wright said in a club statement.
"Brad's commitment to see out the final two weeks of the season speaks to his dedication and care for those around him.
"He is a great football person, well respected right throughout the industry, and we wish Brad the very best for what the next chapter holds for him."
Lloyd's father John played for Carlton and one of his brothers is Essendon great Matthew. Brad played 11 games for Hawthorn before working at Fremantle for 11 years and then joining the Blues.
"It has been a privilege to see the growth of our football program over the last seven years, to arrive here at the end of a two-win season in 2018 and progress to finals and a preliminary final," Lloyd said.
"It has been off the back of an incredible amount of hard work from so many good Carlton people.
"The best part of this job is seeing people growing and working so closely together to strive to achieve a common goal, and I want to sincerely thank all of our staff for their contribution towards that.
"It has been an honour to lead this football department and work for the same club my father represented. I firmly believe it is full of great people with great values, and strong foundations have been established here to take the club forward."
Wright will officially take over from Brian Cook as Blues CEO on Friday.
"Since last October I have been fortunate - through the support of Brian and the board - to gain a thorough understanding of every aspect of our football club," Wright said.
"In recent months, particular attention has been given to the football department in order to gain a comprehensive understanding of our AFL program.
"While clearly our primary focus is on improving football performance - and despite excelling in other areas across the club - my observation is that there is great upside to enhance the connection and integration with our supporters.
"We want to earn respect in this competition, making our people proud to wear the monogram."