Williams' agent, Jill Smoller, confirmed the engagement in an email to The Associated Press.
Ohanian wrote on his Facebook page, "She said yes."
Williams, 35, has been dating Ohanian, 33, for over a year.
Her poem :
"I came home/A little late/Someone had a bag packed for me/And a carriage awaited/Destination: Rome/To escort me to my very own "charming"/Back to where our stars first collided/And now it was full circle/At the same table we first met by chance/This time he made it not by chance/But by choice/Down on one knee/He said 4 words/And I said yes."
Williams in July won Wimbledon for the seventh time to tie Steffi Graf's record of 22 Grand Slam titles. In September she passed Roger Federer for most all-time Grand Slam match victories, winning her 308th in the US Open.
No wedding date has been announced.