Ernie Merrick has plucked the 26-year-old striker from the New Zealand Football Championship as a replacement for injured star Paul Ifill
Krishna, 26, is contracted to the Phoenix until the end of the 2013-14 season as an injury replacement for Paul Ifill who ruptured an Achilles tendon in the 1-0 win over Sydney FC on December 22 last year.
"When we played Auckland City pre-season the two players who stood out for me were Albert Riera and Roy Krishna," Phoenix head coach Ernie Merrick said.
"Riera did a good, simple job in midfield winning the ball and passing it well, and he has made the transition from ASB Championship to A-League with some top-class performances.
"Krishna was quick with close technical skills and an eye for goal, and when I researched his record I was impressed.
"He seems the sort of player capable of taking the next step and scoring goals in the A-League."
Krishna has scored 14 goals in 22 appearances for Fiji, while at Waitakere United, who he joined in 2008, he netted 72 times in 103 appearances.
In the Oceania Football Championships he scored 16 goals in 27 games, while in the Northern League it was 17 in 32.
Despite that impressive record, Krishna shouldn't expect to walk straight into the Phoenix' starting XI.
"At the Phoenix everyone works hard to get a place in the starting team," Merrick said.
"If you do well at training you get on the bench; come off the bench and do well and you get a start.
"Roy will get every opportunity; it is up to him now to grasp it."
That scenario is fine with Krishna who said that in joining the Phoenix he was realising a dream.
"I've always dreamt of playing in the A-League for the Wellington Phoenix," Krishna said.
"I can't wait to get to Wellington and start working with the team.
"I love scoring goals and my goal is to get in the team and do just that.
"I am up for the challenge and really pleased that Auckland City have allowed me to take up this opportunity.
"They always said that if a professional club came for me they would let me go and they have kept their word."
Krishna will train with the Phoenix for the first time on Wednesday.
Northcote City striker Milos Lujic has also joined the Phoenix, signing a two-week contract as a replacement for Reece Caira who is in Oman with the Australian under-22 squad.
Lujic, 23, scored 19 goals in Northcote City's title-winning campaign last season, earning him a reputation as one of the most lethal strikers in the Victorian Premier League.