Meaning: Someone who thinks as I do (definition).

Example: Comparing favorite movies, I found she was a woman after my own heart. (Example in song lyrics.)

Origins: The Bible, Samuel 13:14 and Acts 13:22 (source).

Rewrites:

shares my heartbeat whose pulse beats with mine has similar vibes is tuned into my wavelength

Discussion: It's someone who shares your heart, your sympathies, your beat, your senses... these are just the beginning of ways you can redefine what is a lovely but limited expression of oneness with another person.

I'm changing the format trying to share more research and help you do more with the sentiment behind the idiom. Let me know what you think about the changes.