Former Bury defender Lucketti was a long-time team-mate of Alexander's at Preston during his playing days.
The pair headed up the Deepdale outfit's youth set-up from the start of this season and Alexander was granted permission to take his colleague across Lancashire with him when appointed as Micky Mellon's successor at Town last week.
Although Lucketti's role among the otherwise unchanged Highbury Stadium backroom staff is yet to be defined, Alexander is delighted to have him aboard.
"Chris is here to support me in my job," he said. "We haven't arranged all the job descriptions and details yet.
"Chris helped me with the youth squad at Preston. I played alongside him for a few years and he's a fantastic character, a good coach, straight up and knows football inside out.
"He's been a loyal person all his life. As well as me coming to Fleetwood, I know that Chris will definitely be a positive for this club going forward."