The Rams previously placed the franchise tag on Johnson, and the deadline for signing such players to long-term contracts was Monday. Johnson will be paid $17 million this season before reaching free agency.
Johnson, who was the Rams' third-round pick in 2012, has recorded 16 interceptions in five seasons, including a career-high seven in 2015.
After the 2015 season, the Rams put the franchise tag on Johnson, at a cost of approximately $14 million, and they let cornerback Janoris Jenkins sign with the New York Giants.
Johnson was slowed by an ankle injury and only intercepted one pass last season, yet he became the first cornerback to be tagged for a second straight season since Charles Woodson in 2005.