The system continued to develop and intensified into Moderate Tropical Storm Bejisa on 29 December, with rapid intensification occurring.

[nb 1] Due to an eyewall replacement cycle, Bejisa weakened, but re-intensified to a secondary peak of 160 km/h (99 mph) on 1 January.

After having moved generally south-southeastward for much of its duration, Bejisa turned to the southwest on 3 January, by which time it had weakened to tropical storm status.

It became a post-tropical cyclone on 5 January after the convection weakened over the center, and Bejisa became extratropical the next day as it meandered southwest of Madagascar.

In late December 2013, computer forecast models began to predict the development and cyclogenesis of a disturbance within the monsoon trough north of Madagascar.

[1] At 1800 UTC on 27 December, the Joint Typhoon Warning Center (JTWC) noted a discrete area of disturbed weather approximately 1,350 km (840 mi) north-northwest of Réunion that corresponded with model forecasts and had the potential to develop.

[4] Upon its designation, the disturbance was analyzed to have an unusually high barometric pressure, based on nearby weather station observations.

[8] At 18:00 UTC that day, the depression intensified to moderate tropical storm intensity, thus receiving the name Bejisa by the Mauritius Meteorological Services.

The agency noted that decreasing wind shear, favorable outflow, and warm sea surface temperatures allowed for the intensification.

[16] The intensification phase of Bejisa was short-lived, as an eyewall replacement cycle resulted in a slight deterioration and fluctuation of the storm's organization and structure.

Despite Météo-France assessing that Bejisa had weakened,[23] at the same time the JTWC estimated that the cyclone had intensified further to reach peak 1-minute winds of 205 km/h (127 mph) on 2 January.

[26] Continued wind shear stripped the convection,[27] coupled with cooler water temperatures, and early on 3 January, Bejisa weakened below tropical cyclone status.

[33] Increasing wind shear displaced the remaining convection west of the center,[34] and Météo-France discontinued advisories on Bejisa on 6 January after the exposed circulation turned more to the south.

The Farquhar Group were particularly affected, as the storm's incipient central region of convection remained over the area for an extended period of time.

[44] The winds downed numerous trees and power lines, leaving an estimated 181,000 people without electricity,[45] and closing roads due to debris.

[41] In the wake of Bejisa, Électricité de France (EDF) deployed 500 personnel and 6 helicopters to restore power on the island.

[49] Farmers were eligible for compensation under the disaster declaration; however, many voiced their skepticism following a lack of follow-through by the government to supply funds after Tropical Cyclone Dumile in January 2013.