The agreement is pending a physical exam.
The Dominican starter had requested a salary of $3.9 million for 2011 and the team offered $3 million in arbitration.
Cueto, 24, went 12-7 with a 3.64 ERA in 2010, establishing career highs in wins, ERA, innings pitched (185.2) and walks allowed (56).
He is 32-32 in his three-year MLB career and has averaged over 30 starts per season.
Enrique Rojas is a reporter and columnist for ESPNdeportes.com and ESPN.com.