The cyclone was first noted on January 5, 1988 as a weak tropical depression to the northeast of Tuvalu, in conjunction with the future Typhoon Roy in the Northern Hemisphere.

Extensive damage was reported in New Caledonia after it was exposed to a prolonged period of storm force winds, with the eastern and southern coasts particularly affected.

On January 5, 1988, the Fiji Meteorological Service (FMS) started to monitor a shallow tropical depression that developed within the monsoon trough about 540 km (335 mi) northeast of Tuvalu.

[4] Over the next two days the Southern Hemisphere system developed further as it was steered towards the south-southwest along an area of high pressure, before it became equivalent to a tropical storm while passing through the Tuvaluan islands.

[3][1][5] As a result, the United States Joint Typhoon Warning Center (JTWC) designated the system as Tropical Cyclone 07P and started to issue advisories on it.

[1] Early on January 11, the FMS reported that Anne had peaked, with estimated 10-minute sustained winds near its center of 185 km/h (115 mph), equivalent to a Category 4 severe tropical cyclone on the Australian scale.

[1] Over the next day, Cyclone Anne turned south and rapidly weakened as it encountered upper-level wind shear, approaching the French overseas territory of New Caledonia.

[1] Late on January 12, Anne weakened into a modern-day Category 2 tropical cyclone, before it made landfall on New Caledonia about 110 km (70 mi) to the north-northwest of Noumea.

[2][6][3] During its early stages of development, Anne passed through the central islands of Tuvalu, causing minor damage to houses and crops such as bananas and coconuts.

[11][13][14] Torrential rain, flooding and storm surge caused damage to houses, crops and property while triggering a landslide on the island of Epi.

[1][17] Within the province of Sanma, severe damage was recorded on Espiritu Santo after Anne flooded huts, unroofed school buildings, uprooted coconut trees and destroyed the main wharf.

[32] The first carried a helicopter that transported Vanuatu military forces, medical teams and supplies to the affected northern islands, especially remote villages inaccessible to larger aircraft.

[12] The European Commission provided Vanuatu with €100,000 in emergency aid to purchase local foods, including rice, preserved meat, and fish, and to distribute it to Anne's victims.

[11][16] Within the Paiti-la-Tonuatua area to the north of Noumea, New Caledonia Air Force helicopters rescued several people who had moved to the roofs of their houses.

[37] The European Commission also provided New Caledonia with €85,000, which was distributed by the United Nations High Commissioner for Refugees in the form of cash donations to the worst-affected families.