The replacement was approved on Saturday by the International Cricket Council (ICC) event technical committee, after Bravo was forced to return home with a hamstring injury, reports CMC.
Johnson, a hard-hitting right-hander, has played 30 One-Day Internationals (ODIs) and scored 869 runs at an average of nearly 29.
He has scored two hundreds and two half-centuries, and last played for the West Indies on the tour of New Zealand in January last year.
The 26-year-old has been in good form in the domestic season, hitting 151 in December in the four-day competition and an aggressive 177 in the one-day tournament last month.
Bravo, meanwhile, was forced out of the tour after picking up a lower-grade tear of his left hamstring while completing a single in the 32nd over of the game against Pakistan in Christchurch a week ago.
He took no further part in the match which the West Indies won by 150 runs, and then missed the fixtures against Zimbabwe and South Africa.
Johnson will join the team in Perth as they prepare for the next game against India next Friday.