The 6-foot-5, 323-pound Saffold, who started 41 of 42 games at Indiana University, is expected to move into the Rams' starting lineup at right tackle.
Saffold, who was the 33rd player selected in April, is expected to play right tackle. Jason Smith, last year's No. 1 selection and the second overall pick in 2009, has moved to left tackle.
Due to a knee injury and a concussion, Smith played in only eight games last year, starting five. The Rams will in essence be protecting Bradford, the No. 1 overall pick, with two untested players.
Offensive coordinator Pat Shurmur seems unconcerned, however. He said Wednesday he is excited by what Saffold and Smith bring to the table.
"I think they're young and talented, so we're excited about what these guys can do," Shurmur said. "They've got fresh legs and they're really good players, so we anticipate they?re going to be very productive for a long, long time."
The Rams also said that they have signed sixth-round pick Fendi Onobun, a tight end from the University of Houston. Onobun played one season of college football after a four-year basketball career at the University of Arizona.
Terms of the contracts were not disclosed.
Wednesday's signings mean only No. 1 overall pick Sam Bradford is left unsigned for the Rams.
Information from The Associated Press was used in this report.