Cosgrove, who last season oversaw Leicestershire’s first Championship win for three years, will be assisted by newly-appointed vice-captain Paul Horton .
New signing Pettini previously led Essex to the Friends Provident Trophy and will lead his new county in the Royal London One-Day Cup and NatWest T20 Blast.
Pettini’s vice captain will be Clint McKay , who has 65 caps for Australia in white-ball cricket and was part of the Sydney Thunder side that won the Big Bash in Australia this winter.
Leicestershire elite performance director Andrew McDonald said: “We have completed our player recruitment for the 2016 season and have now put our leadership group in place for the 2016 season.
— Leicestershire CCC (@leicsccc) February 15, 2016
“Mark Cosgrove will continue to lead us in four-day cricket and Mark Pettini will take the reins in one-day cricket.
“Paul Horton and Clint McKay will support them in their respective roles of vice captain but I am looking for leadership throughout the playing group.
“We had some fantastic candidates in the ranks and the most important thing we are stressing is that you don’t need a title after your name to be a leader.
“We can only name one captain and vice captain in each format but we have lots of experienced players in the ranks and I expect leadership contributions to come from a variety of sources.”