Paulsen, 22, earned a move to AFC Bournemouth after a superb campaign for the Nix last campaign, when he was voted the league's best goalkeeper.
He is the most high-profile of three ex-Wellington players to cross the divide and join the new Auckland outfit, which joins the league this season.
The English Premier League club and Auckland FC are both owned by the same multi-club model under American billionaire Bill Foley.
Previously, under a Football Australia rule known as the "Caceres Clause", an immediate move between co-owned clubs had been banned.
That was until Friday morning, when FA announced it had reviewed the rule, with Auckland FC announcing the signing a half-hour later.
Auckland coach Steve Corica said he was delighted to bring the Auckland-raised Paulsen home.
"He was brilliant last season, and he has just returned from a successful Olympics with the OlyWhites," he said.
"He is athletic, a strong shot-stopper and a commanding presence on crosses. He has also demonstrated superb anticipation and is comfortable playing out from the back off both feet."
The Caceres Clause was brought in following the 2016 transfer of Central Coast's Anthony Caceres, who was bought by Manchester City and immediately loaned to affiliate club Melbourne City, causing uproar.
A FA spokesman said clubs supported a move to scrap the clause, while retaining oversight of payments to ensure fairness.
Wellington chief executive David Dome said his club would seek further information over the deal.
"We don't know what 'player registration and salary cap treatment guardrails' will be in place that APL say will 'balance development of the A-League while ensuring competition integrity'," he said.
The move will deepen animosity between Wellington and Auckland ahead of their derby meetings this year.
Paulsen, who signed a long-term deal with Wellington last November before the life-changing move, previously said he playing for his home town club "didn't really cross my mind at all".
"Wellington is my second home ... the Phoenix have the best resources, the best facilities and overall the best people to help me push and strive to be the best goalkeeper and person that I can be," he said last November.
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