Brie, 26, reportedly became engaged to Alex in March soon after she became a household name for her brilliant performance in the gritty Room.
But she only confirmed the news after her recent appearance on Saturday Night Live after being spotted wearing a diamond sparkler.
A source told Us Weekly that Alex popped the question to the Californian-born actress while they were holidaying in Tokyo.
And, according to the same insider, Brie is keen to start a family “right away”.
The couple has been together for over two years, and Brie recently described the Phantom Planet singer as her best friend.
“Oh man, I mean, he’s the other half of the equation – how can you explain support?
“I mean, it goes beyond anything. He’s just my person, he’s my best friend… Yeah, we love each other.”
Brie has previously described herself, Alex, and her other loved ones as gypsies, insisting she needs people around her who understand her lifestyle.
“I don’t really have any people in my life who aren’t gypsies.
“There isn’t anyone in my life who is going to get upset about how much travelling I have to do, or whether or not I’m available for drinks that night.”
Brie has four films coming out soon: Free Fire with Armie Hammer; Basmati Blues with Donald Sutherland; Kong: Skull Island with Tom Hiddleston; and The Glass Castle with Naomi Watts.
For more on Brie’s breakthrough role in Room and her touching Oscar-night tribute, click here.