Watson, 52, has clashed publicly with Labour leader Jeremy Corbyn several times, most notably over Brexit policy and how to handle allegations of anti-Semitism within the party.
The decision is personal, not political," Watson said in a letter to Corbyn, adding he would continue as deputy leader until December 12 to help Labour contest its election campaign.
Unlike other British political parties, Labour deputy leaders are elected by party members and have an independent power base.
A leading centrist and pro-European voice within the Labour Party, Watson had previously lent his support to a second Brexit referendum.
In a letter posted online Wednesday, Corbyn thanked Watson for his contribution to the Labour Party.