American Williams, 39, has rediscovered her best form at Melbourne Park but faces a tough test against Osaka.
She has not played Osaka at a Grand Slam since the Japanese beat her in a dramatic 2018 US Open final.
The match was overshadowed by Williams' argument with umpire Carlos Ramos.
Williams called the umpire a "thief" after he deducted a point from her, and Osaka was reduced to tears by the crowd booing during the presentation ceremony.
"I think we both have had closure, and we have reached out to each other," Williams said of the match.
"I have definitely reached out. I think she's a great competitor and she's a cool cat."
Third seed Osaka, 23, has won a further two Grand Slam titles since that meeting - including the Australian Open in 2019 - but lost the last match she played against Williams in straight sets at the Canadian Open later that year.
Williams, the 10th seed, has shown great form in Melbourne as she aims to equal Margaret Court's 24 major singles titles and reached the semi-finals by seeing off second seed Simona Halep in straight sets.
Both players have only dropped one set so far this tournament.
Their match on Rod Laver Arena will begin at 03:00 GMT on Thursday - and with the lockdown in Melbourne set to be lifted will be played in front of a restricted number of fans.
In the other semi-final, American 22nd seed Jennifer Brady takes on Czech Karolina Muchova, with both aiming to reach a Grand Slam final for the first time.
Muchova, the 25th seed, produced a shock when she knocked out world number one and home favourite Ashleigh Barty in the last round.