The team announced that Ellis signed a $3.5 million, two-year deal. Weber signed for three years and $13.5 million.
Ellis, who led the league in save percentage with .924, will likely be teamed up with prospect Pekka Rinne in training camp. The 28-year-old goalie was signed as a free agent last July and was a key part in Nashville's late-season run to clinch a fourth consecutive playoff berth.
In the 2007-08 season, Weber established a career high in average time on ice with 19:29. He also tied personal bests in shots with 152 and game-winning goals with two. He missed 28 games because of injury.
In 161 career NHL games, the 23-year-old Weber has amassed 70 points and 161 penalty minutes.