The former Doncaster Rovers boss, unveiled as Owls manager this afternoon, has brought in Jamie Smith and Paul Williams.
He confirmed that Thompson and Bullen, who oversaw a spell of results that has given the club a fighting chance of survival in the Championship, will continue their work at the club.
They have a combined 21 years of coaching experience at the club, which Moore hopes to tap into as he sets his stall out at Middlewood Road.
Thompson was pictured at Moore’s first training session with the players this afternoon.
“Both men I know really, really well,” Moore told The Star. “As the chairman amplified, we thank them for the tremendous work that they’ve done here.
“Bully will continue his work with the academy and Thommo will be in between the academy and first team and will keep that connection. I’ve got to have that connection with the younger players because we have one or two wonderful prospects coming through and I’ve got to know about them.
“That’s always been my mantra and as I’ve said before, however you deem it, whether it’s the most experienced player or the youngest, there’s improvement for them all. For me, the slate is wiped clean for them all so I need to know who is in the building.
“It’s important both men keep that information going between the first team and the academy.”