After Rangers won 1-0 at Aberdeen, Celtic responded in emphatic style.
Edouard converted Greg Taylor’s cross before the Scotland left-back laid on a tap-in for right-back Jeremie Frimpong.
Scott Martin’s deflected strike gave Hamilton hope, but Edouard added two more from close range after the break and Patryk Klimala completed the rout.
On the day they unfurled the Premiership flag to celebrate their ninth title in a row – complete with fireworks in the empty stands – Neil Lennon’s side looked vulnerable early on.
Andy Winter tested Scott Bain from distance and David Moyo glanced a header just wide as Hamilton impressed.
Martin’s shot – deflected in off Christopher Jullien – was no less than they deserved as they went in 2-1 down at half-time.
But thereafter, Celtic looked imperious, with Edouard’s clever movement allowing him to net two further simple goals, getting on the end of James Forrest’s cross for his second and Celtic’s third, then pouncing on a rebound to complete his hat-trick.
Frimpong’s pace and skill was another highlight, as he too finished from six yards for his team’s second after a curled cross from his fellow full-back Taylor, and his driving run initiated the move for Edouard’s opener.
Substitute Klimala capped a powerful attacking performance from Celtic as he got on the end of a defence-splitting pass from Jullien to slide his first goal for the club past Ryan Fulton.
Celtic manager Neil Lennon: “Odsonne’s got off to a brilliant start, three strikers’ goals.
“It’s pivotal we hold onto him, we don’t want him to go anywhere. That’s what’s pleased me over the last 12 to 18 months, his goal return as well as all the other things he brings to the game.”
Hamilton head coach Brian Rice: “I am disappointed to lose five goals, but Hamilton will not be judged in games against Celtic.
“We created a lot of chances and we scored as well, but you have to be clinical and you’ve got to keep the back door shut.”
