League sources told ESPN and NFL Media that Floyd is signing a one-year, $10 million contract worth up to $13 million with the Rams. According to ESPN and NFL Media, Whitworth agreed to remain with the Rams on a three-year, $30 million deal.
Whitworth, who will earn $12.5 million fully guaranteed, could make up to $37.5 million, according to NFL Media. His agreed-upon contract is the highest-paying pact signed by a non-quarterback above the age of 35 in league history.
The Rams have yet to confirm the agreements.
Floyd, who turns 28 in September, became a free agent after the Bears released him Tuesday. The No. 9 overall pick in the 2016 NFL Draft out of Georgia started 54 games and recorded 18.5 career sacks for the Bears, but he struggled to consistently pressure opposing quarterbacks.
Floyd notched a career-low three sacks last season. He will replace former Rams pass-rusher Dante Fowler Jr., who agreed to a three-year contract with the Atlanta Falcons on Wednesday.
Whitworth, who turned 38 in December, is entering his 15th season in the league. He is a four-time Pro Bowl selection and three-time All-Pro choice.
Before joining the Rams in 2017, Whitworth played 11 seasons for the Cincinnati Bengals, who selected him in the second round of the 2006 draft.