The 'Summertime Sadness' star reportedly accepted the Scottish singer's proposal last summer, but they have been keeping it secret, according to Us magazine.
The pair first sparked engagement rumours in July last year when Lana, 27, was spotted with a huge diamond ring on her wedding finger while they were house hunting in Los Angeles.
The 'Video Games' star and Barrie - previously singer in the folk-rock band Kassidy, but now thought to have left to perform under the name Nightmare Boy - first got together in 2011.