The 25-year-old won silver in the individual sprint and keirin as well as bronze in the team sprint at the Paris Games.
Richardson was born in England before moving to Western Australia aged nine and is returning to the UK to live permanently having retained dual citizenship.
"I have made the decision to pack up my entire life and move halfway across the world to begin the next chapter in my cycling career," said Richardson, whose nationality switch has been approved by cycling's governing body the UCI.
"It is with a sense of excitement and renewal I announce I have joined the Great British cycling team.
"Switching nationality was a difficult decision and not one I took lightly. It was a personal choice, made after careful consideration of my career and future."
Jesse Korf, the executive general manager of performance for AusCycling, said the move had come as a "surprise" and it was "disappointing that Richardson would be leaving a programme that had delivered great personal and national success".
Richardson was a double gold medal winner at the 2022 Commonwealth Games and has five world championship medals, including gold in the 2022 team sprint.
