The 21-year-old looks set for a move to the City Ground in a deal that could be worth €1.3 million (£1m) after failing to break into the first team at the Emirates Stadium
Lansbury has made just seven appearances for the Gunners since stepping up the first team squad in 2007, spending time on loan at Scunthorpe, Watford and Norwich, and the whole of the last campaign at West Ham.
He now looks set for a switch to the City ground and tweeted on Tuesday afternoon: "Medical done."
It is thought Forest's offer was accepted by the Gunners over the weekend and Lansbury will officially complete the move tomorrow, with Sean O'Driscoll's men to take on Wigan in the League Cup on Tuesday evening.
If Lansbury does indeed move to the City Ground, he will become Forest's ninth summer signing as the Al-Hasawi family look for a Championship promotion push following their summer takeover of the club.