Moyes told evertonfc.com: "Hull have started the season well, they have had some really good results and are dangerous and I think Phil Brown has done a great job there in how he has got them going.
"When he was with Big Sam (Allardyce) at Bolton I came across him alot and I know him quite well. He has worked really hard to get to the position they are in.
"I have been there (KC Stadium) to watch games but never taken a team, so that's new - it will be good for Hull and we are looking forward to it."
The weekend trip is the third consecutive away match in which Everton will have taken on a newly-promoted side.
"I have always thought the start of the season is not a great time to play the newly-promoted teams but we have done fine with the teams we have played so far," noted the boss after wins over West Brom and Stoke.