Sources close to the couple tell TMZ ... the "Spider Man" star popped the question between Christmas and New Year's ... dropping to one knee in a very intimate setting in one of Zendaya's family homes in the United States.

We're told Tom didn't make a huge show of the engagement -- it wasn't a big, over-the-top proposal -- instead, it was very romantic and intimate.

Our sources say the family wasn't there ... it was just a sweet moment between Tom and Zendaya.

Zendaya showed off her massive engagement ring Sunday at the Golden Globes ... and it looks like Tom spared no expense, because the diamond is HUGE.

Tom and Zendaya started dating back in 2021 ... several years after meeting on the set of "Spider-Man: Homecoming."

They instantly became one of Hollywood's most beloved couples ... even though they're extremely private and rarely comment on their relationship.

Our sources say Tom and Zendaya haven't started planning their wedding yet ... they've both got a lot of Hollywood projects and commitments coming up, so we're told it will be a bit before they dip into wedding planning.