Mulligan, 26, joins the Phoenix on a two-year deal after a long career in England, including two seasons with Scunthorpe in the Championship, one step below the Premier League.
Mulligan can play left back or right back - as well as midfield, giving coach Ricki Herbert some options.
He is the eighth new face at the club who debuted in the A-League last year.
With Mulligan's signing, the Phoenix have one spot left on their maximum 23-man roster.
The A-League begins in just under four weeks.