Weir joined the Everton coaching staff midway through last season.
Naismith, 25, said: "When I moved to Rangers Davie Weir was there. I respected him a lot for what he'd done in football.
"He's one of the nicest guys you could meet. I learned a lot from him and I used to ask him questions about his time here.
"Like Rangers he said the facilities are brilliant, that the manager expects you to put in your all, but he's fair.
"He said there are a lot of things that make Everton feel the same in that sense.
"I spoke to Jela a couple of times in the past week and he reinforced what Davie Weir had said on how good the club is.
"As for Duncan (Ferguson), I first met him years ago when I was away with Scotland's Under-19s at Everton's old training ground.
"Being an idol of mine it was great to meet him and to see him this morning and have a chat."