Ghosh has been an old RSS hand and was a state BJP general secretary after joining the party some time back.
Sinha, whose term ended in September, has been made a national secretary, a BJP statement said.
His appointment puts an end to months of speculation as the party mulled whether to let Sinha continue till the polls or replace him as demanded by many West Bengal leaders, who had argued that BJP was steadily losing its support after putting up a strong show in the 2014 Lok Sabha elections and needed a leadership change.
BJP had fetched close to 17 per cent votes, its highest, in Lok Sabha elections in the state and the party had then hoped to consolidate its gains to emerge as a major challenger to the TMC.
However, its dismal showing in subsequent local elections have made things more difficult for it, political watchers believe.