The All Whites, looking to book a spot at the soccer showpiece for the third time after 1982 and 2010, host the South Americans in the opening leg in Wellington next Saturday before travelling to Lima for the return on Nov. 15.
Tenth-ranked Peru are 112 places higher in the FIFA rankings so the return of West Ham United defender Reid after a calf injury and Burnley forward Woods from a hamstring problem are major boosts for the Oceania champions.
"The goal for our squad is simple, we need to deliver the best performance of our campaign and if we do that then we have a good chance of qualifying for the World Cup," said Englishman Hudson.
Rory Fallon, who scored the winner when New Zealand beat Bahrain in an intercontinental playoff to secure a place at the 2010 World Cup finals, was also included in the squad.
Hudson said Fallon, now 35 and plying his trade in the English seventh tier with Dorchester Town, had been called up with fellow veteran Jeremy Brockie as much for their experience as their quality on the field.
"Ever since I arrived here in New Zealand, football people in this country have told me about how special that night was in 2009 when we beat Bahrain to make a World Cup, now we have our chance," Hudson added.
"We can't wait. Our goal is to deliver a performance that will make New Zealand proud."
Peru captain Paolo Guerrero looks set to miss both legs of the tie after being handed a preliminary 30-day ban for testing positive for a stimulant after a match against Argentina on Oct. 5.
New Zealand squad:
Goalkeepers - Stefan Marinovic (Vancouver Whitecaps, Canada), Max Crocombe (Salford City, England), Glen Moss (Newcastle Jets, Australia)
Defenders - Michael Boxall (Minnesota United, United States), Kip Colvey (San Jose Earthquakes, United States), Andrew Durante (Wellington Phoenix), Dane Ingham (Brisbane Roar, Australia), Winston Reid (West Ham United, England), Storm Roux (Central Coast Mariners, Australia), Tommy Smith (Ipswich Town, England), Themi Tzimopoulos (PAS Giannina, Greece), Deklan Wynne (Vancouver Whitecaps)
Midfielders - Clayton Lewis (Scunthorpe United, England), Michael McGlinchey (Wellington Phoenix), Marco Rojas (Heerenveen, Netherlands), Ryan Thomas (Zwolle, Netherlands), Bill Tuiloma (Portland Timbers, United States)
Forwards - Kosta Barbarouses (Melbourne Victory, Australia), Jeremy Brockie (Supersport United, South Africa), Rory Fallon (Dorchester Town, England), Monty Patterson (Ipswich Town), Shane Smeltz (Borneo, Indonesia), Chris Wood (Burnley, England)
(Reporting by Nick Mulvenney; Editing by Amlan Chakraborty)
