I would get the tyres off the rims, then buy 1 pair of 20mm spacers.
With just the alloy wheel without the tyre it will be a lot easier to work out how much spacing you will need, you can swap the spacers front and rear just as a starting point to work out the correct offsets that will work for you and go from there.
I just did a tyre size comparison check from what i running now to what you have got
Mine 245/40/19 = 26.7" diameter
You 245/35/21 = 27.8" diameter
So the 21's will fit in the arch it all depends on the correct spacing.
Check Offsets here
https://tiresize.com/wheel-offset-calculator/

 

How do I find out what the offset is for the current 21 inch wheels?

 

Given what you wrote in your first post then your fronts would be ET22 and rears ET32

9x21 vorne 245/35R21 Reifenpreis bei ReifenDirekt.de anzeigen ET 22 18,20

10x21 hinten 285/30R21 Reifenpreis bei ReifenDirekt.de anzeigen ET 32 18,85

I used this site for reference:
Felgen-Katalog - BMW-Treff - der Treffpunkt für alle BMW-Fans und -Fahrer

 

Ok so I put the front wheel on to see if it would fit and it did. The issue is that it is rubbing against the springs and may be rubbing in another area. I'm confused on why the wheel is so big on the car. I've seen 22s on e60s and it had more room than I have.

 

You need to step the sidewall down, 30 might do it
You are way beyond spec with that size tire

 

Looks like you need to stretch the tyre to fit maybe try 235/30/21, it also looks like you might only need a 10mm spacer up front

 

Ok so i bought a 2 pack of 30mm spacers and I put them on one side of the car. The wheels fit on the car but the front tire is rubbing on the fender. There is no gap between the front tire and the fender.

Would a tire downsize fix the issue?

 

I can't believe you're still trying to make those 21 inch wheels fit! Even if you're successful, you're not gonna to love the ride.

 

I like your old(bronze) set way better