The club said last month that Gonzalez would take charge of the team once he secured the necessary U.S. work permits.
Guillermo Hoyos, who was previously overseeing Miami's professional development structure, had taken over as interim boss after Javier Mascherano stepped down in April.
Gonzalez will take over a Miami squad that has recently suffered disappointing results despite boasting Lionel Messi and a host of established players.
The reigning MLS Cup champions have just one win in their past five regular-season matches. They sit second in the Eastern Conference, nine points behind Nashville.
Gonzalez earned 56 caps for Argentina from 1995 to 2005 and his playing career included spells with Inter Milan, Valencia and Rosario Central. The 52-year-old moved into coaching in 2020 and has since managed several clubs in Argentina.
Gonzalez was scheduled to lead his first training session on Tuesday morning, ahead of Miami's Campeones Cup clash with Mexican side CD Cruz Azul on Wednesday.