The best way to address stiff horses is to start them stretching. Of course, firstly, make sure that he doesn't need to be seen by an equine chiropractor, or in pain from poor saddle fit, etc. Always rule out those issues first, before asking him to stretch in exercise.
On the ground, you can do some "horse yoga" to get the ball rolling. There are several different stretches to target different muscle groups. This video is a great starting point:
In the saddle, make sure that you are actively encouraging him to flex and bend through his whole body by riding correct circles and turns. Start at the walk - if he's stiff at the walk, it won't get better with speed. On the left rein (turning to the left, or traveling counterclockwise around the arena), apply your left (inside) leg at the girth to encourage him to bend through his ribcage around that turn, your right (outside) leg slightly behind the girth to keep the haunches from falling out - that is, as a guard. In terms of the hands, your outside (right) hand is going to maintain a steady and supportive contact, allowing the bend to happen. The inside hand can direct a little more, perhaps lifting slightly if the horse begins to drop his inside shoulder - if he does this, check to see if you're dropping your shoulder as well.
Start with larger turns and circles, and therefore "gentler" bending. 20 meter circles and figure-8's are a good starting point. A great resource is 101 Dressage Exercises: http://www.amazon
If that sticky canter lead isn't a result of a chiropractic issue or other physical problem, it should improve somewhat as he becomes more supple in general. Also, the way the horse is set up for the canter transition can make or break the success of the movement. I highly recommend reading though this thread: Applying aids from walk to trot to canter.
Hope that is somewhat helpful to you, and Good Luck!