Kanye West & Kim Kardashian -- Yeezus! They're Engaged with a 15 Carat Rock

The engagement comes 4 months after Kim and Kanye's daughter North was born -- and 18 months after they went public as a couple.

Monday was Kim's 33rd birthday. This will be her third shot at "til death do us part," and Kanye's first.

BTW -- In case you're interested, it costs $35k to rent out the field. We're guessing he can afford it.