Storer will move to St Andrew's on a six-month deal, to start when the transfer window reopens in May.
The 18-year-old will initially feature for Blues' development squad, having previously been part of the club's academy until Under-15 level.
He became a Stevenage scholar in 2014, signing his first contract last year.
Storer has made one first-team appearance for Stevenage, as a late substitute in their 3-0 league defeat at Leyton Orient last August.
Meanwhile, fellow teenager David Popa, also 18, has become the latest Blues academy player to sign professional terms.
The Romanian striker, who has scored three times in seven games on loan at Kettering Town in the Northern Premier League, follows the lead of free-scoring academy striker Ronan Hale in agreeing a new deal.
Find all the latest football transfers on our dedicated page.
Birmingham City have signed promising teenage striker Jack Storer from League Two side Stevenage for an undisclosed five-figure fee.