Both WD40 and Goo Gone work, need to spray on and let it soak then use a plastic scraper to remove what you can, 12 to 24hrs is best.
Then reapply WD40 or Goo Gone and let is soak again for awhile (hour or so) and use a stiff nylon brush to get the rest off.
After this I cleaned inside of wheel with mineral spirits and used some Meguiar's Ultimate Compound with a high speed polisher and buy hand to get them looking like new again. Wash with a dish detergent to cut any remaing grease and rinse thoroughly.
Now the new tires can be mounted and balanced like new rims.
If you wax inside of rims before you put back on car (after they are balanced so weights can stick) that will help keep dirt and brake dust from staying on rims and should rinse off with normal washings of car and rims.
Well worth the effort to keep your rims looking like new and with the open spoke design it gives a nice detailed look.
I might be anal but a nice set of clean rims can make any car look better.