Tracking northeastward, the disturbance organized over exceptionally warm sea surface temperatures; the Joint Typhoon Warning Center (JTWC) upgraded the system to a tropical depression on 15 May while the India Meteorological Department (IMD) followed suit the following day.

The storm began an eyewall replacement cycle shortly after it reached its peak intensity, but the continued effects of dry air and wind shear disrupted this process and caused Amphan to gradually weaken as it paralleled the eastern coastline of India.

[1] During 13 May 2020, an area of low pressure developed over the Southeastern Bay of Bengal about 1020 km (635 mi) to the southeast of Visakhapatnam in the Indian state of Andhra Pradesh.

[10][11] During 16 May, the India Meteorological Department (IMD) reported that the area of low pressure had developed into a depression and designated it as BOB 01 while it was located about 1,100 km (685 mi) to the south of Paradip in the Indian state of Odisha.

[17] Through the day, the effects of wind shear and dry air hampered this internal core change, causing the eyewall to erode by late on 18 May.

Around 5:30 p.m. IST (12:00 UTC), Amphan made landfall as a Very Severe Cyclonic storm near Bakkhali, West Bengal with winds of 155 km/h (95 mph).

Amphan's forecast track placed 38.9 million people in India and Bangladesh at risk of exposure to the storm's winds, according to the US Pacific Disaster Center.

[24] Ships and aircraft of the Indian Coast Guard directed fishing boats to harbour in coordination with the administrations and fisheries departments of Odisha and West Bengal.

[30] Public works departments were called upon by the government of Odisha to ensure infrastructure resiliency;[31] crews and backup systems for electricity and telecommunications were deployed to meet these needs,[32] establishing helplines for emergency response.

[48] The National Disaster Management Authority advised that these crews and other first responders would also need personal protective equipment and N95 masks due to the ongoing pandemic.

[51] The Bangladesh Cyclone Preparedness Programme and National Disaster Response Coordination Group convened on 18 May to outline preparations for Amphan.

[52] Several non-governmental agencies coordinated with the Cyclone Preparedness Programme to support Rohingya refugees at camps in Cox's Bazar during Amphan.

[29] According to Inter-Services Public Relations, 145 disaster management teams from the Bangladesh Armed Forces were placed on standby with special equipment.

[57] The Ministry of Agriculture of Bangladesh advised coastal farmers to harvest all mature paddy fields to mitigate the estimated loss of 12 percent of crop yield.

[69] Odisha Chief Secretary Asit Kumar Tripathy initially identified 403 possible cyclone shelters in areas potentially impacted by Amphan, though 105 served as temporary medical centres for quarantines associated with the concurrent COVID-19 pandemic.

[71] The Kolkata Municipal Corporation located schools and community centres for possible use as temporary shelters to augment evacuation capacity.

[75][76] More than 12,000 shelters were opened across Bangladesh, supplied with food and emergency cash from the Bangladeshi Ministry of Disaster Management and Relief and yielding capacity for 5.19 million evacuees.

[77][78] There were 5,767 more shelters in Bangladesh for Amphan than for Cyclone Bulbul, which struck the country in November 2019, due in part to social distancing restrictions.

[90] Officials farther inland in Dhanbad and Bokaro Steel City, Jharkhand, were also instructed to move people from susceptible housing to safety.

[70] Amphan made landfall near Bakkhali in West Bengal at 2:30 p.m. IST on 20 May,[19] buffeting the region with strong winds and heavy rains.

[117] Strong winds inflicted severe damage in Kottayam district, especially in Vaikom taluk, where homes and temples were impacted and trees and electric poles were downed.

[93] Nearly 220,000 homes were damaged, of which 55,667 were destroyed, rendering an estimated 500,000 people homeless according to the United Nations Office for the Coordination of Humanitarian Affairs.

[131] All 65 freshwater ponds in the Sundarbans were inundated by saltwater and numerous kewra trees were uprooted;[126] however, damage to the mangrove forest was less than initially feared.

[133] The Department of Fisheries estimated that ৳2.17 billion (US$25.6 million) in losses to crab, finfish, and shrimp were sustained by 40,800 farmers due primarily to the flooding of farms.

[136] The cyclone produced heavy rainfall and strong winds in Sri Lanka while intensifying east of the island, affecting some 2,000 people and triggering floods and landslides.

[140] Stemming from damage to fibre-optic cables in Kolkata, Bhutan Telecom saw a total loss of service for 17 hours on 20–21 May and TashiCell saw a 60 percent outage.

[106] Approximately 1,000 ground teams worked to restore infrastructure and services in West Bengal after Amphan, though only 25–30 percent of workers were staffed due to the COVID-19 pandemic.

[95] The resulting slow restoration of power sparked protests across West Bengal aimed primarily at electricity company CESC.

[148] The Home Department of West Bengal requested additional crews from railway and port interest, while five brigades from the Indian Army were deployed in Kolkata and the 24 Parganas districts to support recovery efforts.

[106] The Ministry of Disaster Management and Relief in Bangladesh approved a ৳2.5–3 billion (US$29–35 million) budget to repair embankments damaged by Amphan.