Hockaday, whose only previous managerial role was with Conference outfit Forest Green Rovers, emerged as a contender early this month when bookmakers made him favourite for the role.
That was met with disapproval from many Leeds fans who were hoping that owner Massimo Cellino would opt for a more experienced coach to replace Brian McDermott.
However, the Italian has pressed ahead and secured the 56-year-old's services on a two-year deal.
While his appointment has been met with widespread opposition from the club's supporters, Hockaday is backing himself to prove the doubters wrong.
"Is it a surprise?" said Hockaday in an interview on Leeds' YouTube channel.
"It isn't because of my background and the fact that I'm a very experienced coach and the fact that the president wants an experienced British coach, then I seem to tick all the boxes.
"At the end of the day I've been given this great opportunity and I intend to take it with both hands."
He added: "I've already talked to the president about a number of players and a number of positions that we've identified where we need to strengthen, so there will be changes."
Hockaday was part of Aidy Boothroyd's backroom team when Watford beat Leeds in the second-tier play-off final at Wembley in 2006.
Leeds finished last season 15th in the Championship and have now spent a decade outside of the Premier League.
Junior Lewis, the former Gillingham midfielder, has been named as Hockaday's assistant.