The West Bromwich East MP was handed the position in September 2015, but has now been replaced by Ian Lavery, a campaign co-ordinator and key ally of the Labour leader.
The Labour Party Chair is a courtesy position that was created by Tony Blair in 2001.
Mr Corbyn said the appointment of Mr Lavery would 'strengthen our campaigning and party organisation, as we prepare to contest a new general election and form the next government'.
Mr Watson, who is Labour's deputy leader, will continue as the shadow culture secretary.
In last week's General Election he retrained West Bromwich East with a reduced majority of 7,713.
In other shadow cabinet changes Owen Smith, a former leadership challenger to Mr Corbyn, was handed the work and pensions brief.
And new MP Lesley Laird was made shadow Scottish secretary, while Andrew Gwynne will serve as shadow communities secretary.