The tennis star made the announcement in the form of a poem.
She said he took her to Rome, where they first met, to propose to her - and she said yes.
It caps off a year in which Ms Williams won her seventh Wimbledon singles title and 22nd Grand Slam singles title, but dropped to world number two ranking.
Reddit is a social media community where users group around topics, news articles and discussion points, rather than around people they know in offline life.
Mr Ohanian founded it in 2005 alongside a college friend, Steve Huffman.
Ms Williams posted to r/isaidyes, a forum where users share their stories of wedding proposals, saying he had taken her to the table in Rome where they first met, where he got down on one knee and "said four words".
Mr Ohanian and Ms Williams had kept their relationship quiet on social media and in the world of celebrity gossip, but rumours began to circulate last year that they might be romantically linked.