Millions of people were evacuated in anticipation of the storm, which originated in the Bay of Bengal.
The storm, the first super cyclone in the area since 1999, is forecast to cause deadly storm surges, severe flooding and mudslides.
The coronavirus and social-distancing measures have made mass evacuations more difficult for authorities.
India's weather department said in an afternoon update that Amphan was making landfall in a process that would take several hours.
It has begun hitting the Sundarbans, a mangrove area around the India-Bangladesh border, and will later move north and north-eastwards near the major city of Kolkata in India's West Bengal state, meteorological officials said.
The safety and well-being of BDP employees are our top priorities. Due to BCP previously in place as a result of COVID-19, BDP India teams are working remotely. We do expect some impact on both port and airport operations in Kolkatta. Rest assured we will continue to monitor the situation closely and will share additional updates as we receive them. Should you have any questions or concerns, please reach out to your local BDP representative.