The 21-year-old, who spent much of last season on loan at the City Ground after putting in a transfer request at Albion, is poised to undergo a medical before putting pen to paper on Wednesday.
Forest midfielder Matt Thornhill, 20, is moving in the opposite direction, joining the Seagulls on loan until January.
"He's a young midfielder who has huge potential and Forest rate him very highly," said Brighton boss Russell Slade.
He added: "As a club we wish Joel all the best. Forest retained their interest through the close season and we have agreed a deal which is right for the club."