Barca announced the deal would see them receive six million euros (£5.5m) for the Uruguay international.
The 33-year-old's move is subject to agreeing personal terms and a medical, Atletico said.
Suarez joined Barca from Liverpool in 2014 and helped the club win four LaLiga titles, four Copa del Reys and the Champions League in 2015.
He was reportedly told he had no future at the Nou Camp under new boss Ronald Koeman and had been linked with a move to Juventus.
💙❤️ @LuisSuarez9, Barça legend
🙌 #9raciasLuis pic.twitter.com/WHCeMW4C9p
— FC Barcelona (@FCBarcelona) September 23, 2020
But his next club is set to be Barca's LaLiga rivals Atletico after the two sides came to an agreement.
A Barca statement read: "FC Barcelona and Atletico Madrid have reached an agreement for the transfer of the player Luis Suarez. The Madrid club will pay FC Barcelona six million euros in variables.