The two stood hand in hand as they waited for their car to pick them up

By Jodi Guglielmi
Updated January 11, 2016 01:55 PM
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Credit: X17

And the award for most glamorous couple at the Golden Globes goes to …

Michael Fassbender and Alicia Vikander looked the picture of romance on Sunday night, putting their relationship on full display for their award-show debut as a couple.

Not only did the two exchange a few loving glances as they sat next to each other at the award ceremony, the famously private couple took their PDA to the next level later in the night.

Fassbender, 38, and Vikander, 27, were spotted holding hands as they left an afterparty at West Hollywood’s Sunset Tower Hotel. The two stood hand in hand as they waited for their car to pick them up.

At the NBC Universal party, the two posed for selfies near the bar. An observer told PEOPLE the two were huddled close and seemed to be happy and in great spirits.

But before the award ceremony even began, the actor gushed on the red carpet about his girlfriend’s impressive year, saying he’s “very proud” of her.

Vikander, a double nominee for her performances in The Danish Girl and Ex Machina, wore a pleated white dress with a ruffle trim around her neck. Fassbender – who was nominated for best performance by an actor in a motion picture, drama for his portrayal of the Apple legend Steve Jobs – wore a sleek black tux.

The starry couple, who have remained low-key about their relationship, first met on the set of their film The Light Between Oceans in 2014 and have been romantically linked ever since.