He said the proposal was "super romantic", but he didn't want to reveal any details about it.
Dotcom and Donnelly, an Auckland woman, announced they were a couple last year.
Dotcom revealed the pair were head-over-heels in love.
"I'm in love. We're in love. This is not some fling - this is serious," he said in an earlier interview.
"I thought I would never love again," Dotcom said. "My heart turned ice cold after my separation from Mona. To love and be loved is what happiness is all about. I'm so happy that I met Liz and that I can feel those butterflies again."
The pair have a 21-year age gap.
Commenters on his tweet today shared their congratulations at what appeared to be an engagement announcement, while others were less supportive.
"Do not get married, she will take half your money lmaoooo," one commenter said, while another said "Honestly, I always thought she was your daughter until a few days ago."
Twitter user Ekim Nazim Kaya questioned how Dotcom's potential new fiancee was handling the internet comments.
"@KimDotcom she's not offended from ugly comments your loser haters throw at you guys?"
Dotcom replied, saying the pair loved their "haters".
"They are just fans in denial," he said.
Donnelly earlier tweeted a picture of Dotcom's birthday celebrations, and Dotcom also tweeted a screenshot from a video chat between the two of them, surrounded by love hearts and other emojis.