There was a cloud mass north of Arnhem Land for several days before the surface circulation which was to become tropical cyclone Rebecca was identified. The low formed near 11.4°S, 135.3°E at 0300 U'TC on 20 February 1985 with a central pressure of 1000 hPa. This low drifted northeastwards for about 12 hours before gradually altering course to the southeast during the following 12 hours. Intensification was spasmodic with cyclonic intensity being reached about 1800 UTC 21 February when the centre was at 11°S, 139.8°E. The southeasterly track continued with little further development until landfall at about 0900 UTC 22 February near 12.9°S, 141.7°E on the west coast of Cape York Peninsula.
As a weak cyclone Rebecca lost its cyclonic intensity almost immediately. The resulting low continued to the centre of Cape York Peninsula as a rain influence for about 30 hours before decaying about 300 km west of Cairns. The estimated maximum wind speed was 70 km/h. There was only minimal damage and no significant winds were reported.