Mulligan, 26, joins the Phoenix on a two-year deal after a long career in England, including two seasons with Scunthorpe in the Championship.
The Kiwi international left United in January for Port Vale, but was released by the Valiants at the end of last season.
Phoenix chief executive Tony Pignata was delighted to snap up a player who they have been interested in for some time.
He said: "We've been discussing options with David for a few months and the opportunity came about last week and we agreed terms to a two-year contract. He offers us a lot of versatility given his ability to play at the back on the left or the right, as well as midfield."
"He's played in the Championship, which is an extremely good league," he added. "Unfortunately things didn't work out for him when he went to Port Vale. He had a few options in the United Kingdom but he realised that the A-League was an attractive proposition.
"It just goes to show that, instead of playing in the lower leagues in the UK, you can have a great career in the A-League."