Yes, Expertise affects passive Perception checks.
Passive Checks (PHB 175)
Here's how to determine a character's total for a
10 + all modifiers that normally apply to the check
For example, if a 1st-level character has a Wisdom of 15 and proficiency in Perception, he or she has a passive Wisdom (Perception) score of 14.
Simply put, if you have a WIS mod of +3 and a proficiency bonus of +4 (with proficiency in Perception), your passive Perception score will be 10 + 7, or 17. If you have Expertise in Perception, the +4 is doubled, so you're correct in judging that your passive Perception score will be 21.
Even better, if you're in a context that would grant you advantage on your Perception check, your passive Perception would be no less than 26, thanks to how advantage modifies your passive Perception score:
If the character has advantage on the check, add 5. For disadvantage, subtract 5.