Baldvinsson replaces outgoing CEO Bjorgolfur Johannsson, who is leaving to take a position with Iceland Air Group.
Baldvinsson is the fourth CEO to take the helm at the company the past three years.
Icelandic's board chairman, Magnus Thorsteinsson, said Baldvinsson's role will be to increase profitability and "reinstate [Icelandic] as a leading company in the seafood industry."
Icelandic Group has struggled with rising fish prices and costly, lengthy restructuring.
"The group has gone through turbulence and reconstructions in the operations and it is my assignment to ensure that...objectives