Lansbury, 18, is expected to complete his move to Glanford Park on Monday and will be eligible for the squad to face Southend United on Tuesday night.
He is captain of the England U19 side, where he plays alongside fellow Iron loanee Krystian Pearce, and made four Carling Cup appearances for the Gunners this season.
Nigel Adkins, the Iron manager, is also tracking the Barnsley forward Kayode Odejayi.
He wants to bring the player to the Iron on loan as Ben May's absence through injury means the club are lacking cover for first-choice strikers Gary Hooper and Paul Hayes.
The club have bid for the Gateshead striker Lee Novak, but Huddersfield Town now appear favourites for his signature as they are willing to allow him to remain on loan at the Blue Square North club until the end of the season.