Smith was absent from training at The Oval on Tuesday, with the England and Wales Cricket Board confirming the arrival of his second child earlier that morning.
Rew, the 22-year-old from Somerset, takes over the gloves and will bat No.6 to complete a hat-trick of new faces in an unfamiliar home XI.
Fast bowler Sonny Baker and batter Jordan Cox had already been named in the side, with Rew's addition making a total of five changes from the side which beat New Zealand by 115 runs at Lord's just 10 days ago.
Rew will be the 20th player to make his debut under head coach Brendon McCullum in 46 matches.
Cox and Baker replaced captain Ben Stokes and Gus Atkinson, who were not considered for selection following their breach of a team curfew during last Sunday's victory celebrations, with Jofra Archer and Matt Fisher also coming in to the side.
Rew has long been tipped for full international honours. At the start of last season the left-hander became the youngest Englishman to reach 10 first-class centuries since the revered Denis Compton in 1939 and he has added two more since.
Rew travelled to Australia with Andrew Flintoff's Lions, which he has captained, and spent further time with the senior squad.
He is considered solid rather than outstanding behind the stumps and was put through his paces in a lengthy session with Sarah Taylor, the World Cup winning former England keeper who has become the first woman to work with the men's national team.
ENGLAND (v New Zealand, second Test): Ben Duckett, Emilio Gay, Jacob Bethell, Joe Root (capt), Harry Brook, James Rew (wk), Jordan Cox, Jofra Archer, Josh Tongue, Matthew Fisher, Sonny Baker.
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