The deal is also expected to feature draft-pick compensation heading to the Rams.
Bradford, the No. 1 overall pick in the 2010 draft, has not played in a regular season game since his 2013-14 season ended with a torn ACL. He was on track to start at quarterback for the Rams this season before suffering a second torn left ACL in the preseason.
Like Bradford, Foles ended the 2014-15 season on the sidelines due to injury. Foles suffered a broken collarbone in a Nov. 2 win over the Texans and was replaced by Mark Sanchez, who recently re-signed with Philadelphia.
Drafted in the third round of the 2012 draft, Foles broke out in the 2013-14 season running coach Chip Kelly's up-tempo offense. Foles finished that season with 27 touchdown passes to just two interceptions while throwing for 2,891 yards.