Tripathi was received at Howrah Station by senior West Bengal ministers Amit Mitra and Partha Chatterjee and was given Guard of Honour there by the West Bengal Police, Raj Bhavan sources said.
On arrival at the Raj Bhavan, he was given a floral welcome by the staff of the Raj era edifice and was given Guard of Honour by the Kolkata Police, the sources said.
Tripathi, who arrived by the New Delhi-Howrah Rajdhani Express from Allahabad, was delayed by over six hours owing to rerouting of trains following a blast on railway tracks between Mughalsarai and Gaya late last night.
Tripathi, a former Uttar Pradesh Speaker, would replace M K Narayanan who resigned after being nudged to do so by the NDA government at the Centre.
Tripathi, who will turn 80 in November this year, was a five-time MLA.
Bihar Governor D Y Patil took over as Governor of West Bengal as an additional charge after Narayanan demitted office on July 4.