Rehan's call-up comes after limited success for Leicestershire in this year's County Championship - he's so far claimed just six wickets at 67.66 in ten outings. However, he has made his presence felt for his county with the bat instead, with 423 runs at 38.45, including four half-centuries and a best of 90 against Glamorgan.
He will link up with the squad in London this weekend, ahead of the second Test which starts at Lord's on June 28.
Moeen's own return to Test cricket, after an absence of 21 months, had come in the wake of a back stress fracture sustained by England's first-choice spinner, Jack Leach, which has ruled him out for the entire summer.
His figures of 3 for 204 did not make for especially pretty reading during his comeback, and he was visibly hampered by a sore on his right index finger, which earned him a 25 percent match-fee fine after he was punished for using a drying agent mid-match.
However, speaking after the game, head coach Brendon McCullum indicated that England would do everything they can to get him right for the rest of the series, after praising his contribution - which included the significant wicket of Travis Head, Australia's most attacking middle-order batter, in both innings.
"I'm pretty confident that we can get on top of Moeen's finger," McCullum said. "That will give us an opportunity to select him in the next game and, if he's available, he will be selected. I thought Moeen did a great job."
Other alternatives could have included Liam Dawson, Hampshire's spinning allrounder, who has been in good form for Hampshire in the County Championship this season, and has had prior experience of coming into high-profile squads at short notice, following his call-up for the 2019 World Cup squad.
Will Jacks, the Surrey allrounder who claimed six wickets in his debut Test innings in Rawalpindi in December was another possible pick - he too offers plenty with the bat, and cracked five sixes in an over for Surrey against Middlesex en route to 96 from 45 balls in the T20 Blast on Thursday night.
However, it is understood Root's performance on the final day of the first Test - bowling 13 overs straight up to the second new ball, dismissing Alex Carey in the process - meant the selectors felt they were covered for off-spin, preferring an option who turns it the other way.
His precocity first came to prominence in July 2016 when, as an 11-year-old, he was called down to Lord's to assist England's preparations for facing Pakistan's legspinner Yasir Shah in that year's first Test, and even dismissed Ben Stokes and Alastair Cook during his stint in the nets.
When he returned for the following year's Test against South Africa, his talents even impressed the late Shane Warne, who predicted at the time that he would be "playing first-class cricket at the age of 15".
Andrew Miller is UK editor of ESPNcricinfo. @miller_cricket