Fresh from competing for the Matildas at the 2015 FIFA Women's World Cup, the 27 year-old will link up with the National Women's Soccer League (NWSL) side pending visa clearance.
Heyman played in all five of Australia's World Cup matches in the Matildas' historic run through the tournament in Canada, including two starts.
Among Heyman's new team-mates are USA striker Sydney Leroux and Nigeria midfielder Halimatu Ayinde, who Heyman locked horns with during Australia's memorable Group D 2-0 win.
"Michelle coming in is going to enable us to vary things a little bit more tactically," said Flash coach Aaran Lines.
"She's going to give us some experience in the final third of the field.
"Everyone who has played in that role for us has done a very good job, and we are adding another quality player to our roster - one who has played an important role with Australia."
Heyman is the latest of a number of Matildas stars to continue their careers overseas.
Striker Kyah Simon, who scored three World Cup goals, is also heading back to the United States to spend another season with former club Boston Breakers.
Outstanding midfielder Elise Kellond-Knight has joined German Women's Bundesliga club FFC Turbine Potsdam on a two-year deal.
Kellond-Knight was awarded back-to-back player of the match honours in Australia's group-stage draw with Sweden and Round of 16 win over Brazil.
