The team made the announcement at a Tuesday afternoon news conference, when the Rams also held media access to the 11 players they took in last week's draft.
On Monday, the NFL released sales figures of its best-selling rookie jerseys over draft weekend, and those of Sam -- the first openly gay player to be selected -- sold better than any other jersey except those of Johnny Manziel.
Sam came out as gay in media interviews earlier this year. His Missouri teammates and coaches knew his secret and kept it for his final college season. Sam went on to have the best year of his career: He had 11.5 sacks and was selected SEC co-defensive player of the year.
The 6-foot-2, 255-pound Sam was considered a mid- to late-round pick, far from a sure thing to be drafted. He played defensive end at Missouri, but he's short for that position in the NFL and slower than most outside linebackers, the position he'll need to transition to at the professional level.
He was taken with the 249th overall pick out of 256.
The Associated Press contributed to this report.