The Saints also agreed to terms with tight end David Thomas, general manager Mickey Loomis confirmed Tuesday.
Franklin, who turns 31 in August, has recorded 187 tackles, four sacks, one interception and three forced fumbles in his eight-year career.
The 6-foot-1, 317-pound Franklin is an eight-year veteran and proven run defender who has started the past four seasons for San Francisco after beginning his career in Baltimore. His addition adds depth to an interior defensive line that already includes 6-4, 350-pound Shaun Rogers and 6-1, 307-pound Sedrick Ellis, the Saints' 2008 first-round pick.
The Niners placed the franchise tag on him in 2010 and had hopes of agreeing to a long-term deal but were unable to come to terms with him.
Thomas has been a regular contributor since joining the Saints in their Super Bowl season of 2009, with 30 or more receptions in each of the past two seasons. A strong blocker, he also has played fullback when needed.
The deals came the same day New Orleans agreed to terms with top draft choice Cam Jordan.
Oliver is a four-year veteran who has appeared in 44 games for San Diego. He has 106 career tackles, three interceptions, one forced fumble and three fumble recoveries. He also has been a special teams regular.
Humphrey has been with the Saints the past two seasons after spending his first three pro seasons with Green Bay. He played in six games last season, catching one pass for 12 yards.
Lambert was undrafted in 2009 and has yet to make his debut in an NFL regular season game, but the 25-year-old out of Notre Dame has spent time with San Francisco, Indianapolis, St. Louis and Miami during the previous two seasons.
New Orleans also waived a pair of undrafted rookies who had signed with the club last week but quickly started missing practices because of injuries. One was cornerback Josh Gatlin out of North Dakota State, who was struggling with an injured thumb and knee. The other was guard Carl Johnson out of Florida, who never passed his physical because of a hamstring pull.
Information from The Associated Press was used in this report.