Tony was the first Australian cyclone of the 1979-80 season. It was one of the infrequent cyclones that occur in low latitudes of the Indian Ocean during winter and spring months. On 26 August 1979 a tropical low had developed on a shear line about 1300 km west-northwest of Cocos Island and by 1800 UTC 27 August 1979 it was estimated to have reached tropical cyclone intensity. Tony moved slowly west-southwest and attained peak intensity at about 1200 UTC 29 August 1979. The Dvorak satellite intensity analysis technique gave a central pressure of about 990 hPa and a maximum ten minute mean wind speed at peak intensity of about 95 km/h.
A striking feature of the surface pressure pattern during the lifetime of the cyclone was an intense anticyclone of about 1040 hPa some 2800 km to the south. On 26 and 27 August 1979 a mid-latitude cold outbreak on the eastern flank of the anticyclone (between longitudes 100°E and 110°E) produced a strong surge in the easterly trade winds to the south of the tropical low. This probably aided its development to tropical cyclone intensity. The steep pressure gradient between the tropical cyclone and the anticyclone to the south caused gale force winds to be experienced up to 1200 km from the storm centre. At 0000 UTC 28 August 1979 a ship about 150 km to the southwest reported a pressure of 1002.5 hPa and a sustained wind speed near 74 km/h. There were no reports within 100 km of the cyclone centre. Early on 30 August 1979 Tony crossed longitude 80°E into the Mauritius Region.
Tony occurred west of 90°E when the Australian region extended to 80°E.