Lookman has been exploring his options away from Atalanta in recent weeks and had considered Fenerbahce as a possible destination.
However, the winger was understood to favour a switch to LaLiga, with the opportunity to play under Diego Simeone proving a decisive factor after the terms of a move to Turkey became complicated.
A formal agreement was reached early after that final talks went to plan.
With deal gone through, it will add fresh uncertainty around Alvarez’s future at Atletico, at a time when the club are also trying to sign forward Marcos Leonardo from Al Hilal.
The Gunners have already been exploring the feasibility of a move for the end of the season.
There will be some complication to work out a suitable package to take Alvarez to north London but Arsenal are aware that any move would require careful structuring.