The 28-year-old joined the club for an undisclosed fee on Wednesday following an unsuccessful spell with the Saints.
"Billy is a prolific goalscorer and is tried and tested at Championship level. He was desperate to come here and play for us. I'm delighted to welcome Billy to the club," Hockaday told United's official website.
Leeds return to action on Saturday when Middlesbrough visit Elland Road in the Championship.