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.

The database is reported to contain information on 100,000 US Department of Defense employees, among others.
Troy Hunt, who published news of the leak, said the information had "enormous" potential for scammers.
Business services firm Dun & Bradstreet confirmed to tech news site ZDNet that it owns the data.
Information on government departments and private sector employees is commonly collated by business services that sell the data to other companies, such as marketing firms.
In this case, the records - including names, job titles and contact details - were originally compiled by NetProspex, which was acquired by Dun & Bradstreet in 2015.
Organisations with employees mentioned in the data include the US Postal Service, telecoms giant AT&T and the retailer Walmart.
Mr Hunt pointed out that people might try to use the names and email addresses in the database to scam or retrieve sensitive information from recipients - a practice known as spear phishing.
"The value for very targeted spear phishing is enormous because you can carefully craft messages that refer to specific individuals of influence and their roles within the organisation," he wrote on his blog.
Dun & Bradstreet told ZDNet: "Based on our analysis, it was not accessed or exposed through a Dun & Bradstreet system."
The leak is the latest in a long string of personal data caches dumped online.
In January, personal information of health workers in the US Army was found online by another security professional.
Birmingham City have signed promising teenage striker Jack Storer from League Two side Stevenage for an undisclosed five-figure fee.
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Details of more than 33 million US employees - including military staff - have been released online, according to a security researcher.