"I just got verklempt," Aniston said, wiping tears from her eyes.
Handler seems to be equally happy for her friend. "He's the greatest guy ever," Handler said. "You guys make the greatest couple ever and I'm so happy for you two."
Aniston's appearance on Chelsea Lately marks the first time she's addressed the big news since Theroux blinged out her ring finger in August.
Watch the full interview below to see the emotional Aniston. Plus: Learn where Handler gets all her good ideas (apparently, she's quite the copycat).