The deal includes a player option after the fourth year, sources said.
The deal can't be officially signed until July 7, when a league-wide moratorium on signings and trades is lifted.
After the sides mutually agreed not to do a contract extension last October, making Drummond a restricted free agent this summer, Detroit's No. 1 offseason priority was always securing Drummond as quickly as possible.
The Pistons hold Drummond's Bird Rights, which allow teams to go over the cap to retain their own free agents.