Play video content EXCLUSIVE TMZ.com

'Amazing Race' couple Cody Nickson and Jessica Graf have been through a lot together -- in the public eye -- and now they can add getting engaged to the list.

We got this video of Cody proposing to Jessica at the top of Runyon Canyon Park's hiking trail in L.A. Tuesday ... and there were no shortage of tears flowing when she said yes.

We're told Cody ran ahead of her to make it a surprise, and told the group of people in the area his plan ... which is how he had a nice cheering section. Quality move.

You may recall ... Cody and Jessica met on last season of "Big Brother" and became one of its showmances, but not without controversy. Cody was portrayed as a villain on the show, and Jessica was slammed for unwanted butt-poking of other houseguests.

The 2 always stuck together, though ... and now it appears that's their goal for life.