The Rams also signed sixth-round selection Fendi Onobun, a tight end from Houston who played just one season in college. Terms of the deals announced Wednesday were not disclosed.
Saffold, the 33rd overall selection in the April draft, is expected to make a strong push to start at right tackle.
The lone 2010 draft selection still unsigned is No. 1 overall pick Sam Bradford. The Rams and representatives for the former Oklahoma quarterback have been meeting for weeks.
Training camp opens Thursday for Rams rookies.