A deal has been finalised for the 17-year-old midfielder, according to the Yorkshire Evening Post.
Stevens becomes Leeds’ second deadline day signing following the capture of forward Tyler Roberts from West Brom.
Express Sport reported earlier in the day that Leeds officials were working on a deal for Stevens.
He is believed to have cost the Championship club around £250,000.
Stevens made his debut for League Two outfit Forest Green earlier this season and made 15 appearances in all competitions.
It was reported earlier this month that Premier League sides Brighton and Everton were also monitoring his progress.
Leeds have been busy strengthening their development ranks since Andrea Radrizzani completed his takeover last summer.
Stevens is the fifth Under-23 team signing this month following Aapo Halme, Oliver Sarkic, Pascal Struijk and Sam Dalby in committing his future to the club.