Taylor was appointed to the role in January 2010 after a brief stint as interim chairman, as the Hornets faced cash-flow problems.
With the club now in a stable position both on and off the pitch, Turner has opted to stand aside as he also struggles to devote the time required to the position.
Taylor will also relieve his duties as non-executive director at Vicarage Road, which he has held since January 2009, but will remain as life president.
He told the club's official website: "Having accepted the position of non-executive chairman after being interim chairman, I have always made it clear I never felt this to be something for the long-term."
Owner Laurence Bassini will act as interim chairman until Watford's board arrange a permanent long-term replacement.
Taylor, a lifelong Iron fan having grown up close to the Old Showground, has been vice-president at Scunthorpe since September 2005.
He made his name managing Lincoln, Watford, Aston Villa and England. He will be in Poland and Ukraine this summer to act as a pundit for BBC Five Live.