Lightning general manager Brian Lawton said Friday's signing accomplished an offseason priority of adding an experienced backup goalie.
Niittymaki has played in 161 career NHL games, all with the Philadelphia Flyers, and has a 62-61-23 record. He appeared in 32 games with Philadelphia during the 2008-09 season, going 15-8-6.
Smith missed the final two months last season due to post concussion syndrome. The Lightning have said Smith will be ready for the start of training camp in September.
The team announced both deals on Friday without providing details.
The 24-year-old Sestito made his NHL debut with the Oilers last season, playing in one game and recording a shot on goal. He spent most of the season with Springfield of the AHL.
Danis spent last season with the New York Islanders organization and appeared in an NHL career-high 31 games, posting a 10-17-3 mark and leading the team with two shutouts. The 28-year-old had a .910 save percentage and 2.86 goals-against average.
Previously, Danis had spent four-plus seasons with the Montreal Canadiens' organization.