The Canada youth international, 25, was thrown through the windscreen of a hire car while on holiday in Finland in 2021 as a result of a malfunctioning seatbelt.
The former Liverpool keeper suffered seven neck fractures and had to wear a halo around her neck, doctors fearing she may never play again.
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Foster now hopes to defy the odds once more after signing a deal with Wellington on Tuesday.
"Joining the Phoenix is very symbolic," Foster said. "It's a new becoming. It's an arising from something that was literally in ashes.
"I've been through a lot in the last two years, more than most people go through in their whole lives."
New Phoenix boss Paul Temple said having Foster and Edwards on the books indicated the New Zealand club had arguably "the best goalkeeping pair in the league."
"We've been pushing to have two high quality players in every position so the squad is really competitive," Temple said.
"Brianna was our No. 1 goalkeeper in the league last year, and we wanted to bring someone else in [who] could also be a No. 1 goalkeeper.
"Those two can fight it out and there will be a really good competition for that place. I think that will bring the best out of both of them like it has everywhere else on the pitch."
Wellington, who have picked up the wooden spoon in their first two A-League Women seasons, begin the 2023-24 campaign at home to Melbourne City on Oct. 15.