Everett joined what was then Mori from Ernst & Young 12 years ago, during which time he has been responsible for completing two management buy outs of the Mori business.
He was also responsible for overseeing the merger of the operations of Mori and Ipsos.
Gosschalk has been promoted to CEO of Ipsos Western Europe and joins the management board of Ipsos Group, with responsibility for the global public affairs.
Gosschalk joined Mori in 1979 and was managing director then CEO from 1994 to 2005. He was appointed CEO of Ipsos Mori in 2005.
Ben Page, managing director of Ipsos Mori Public Affairs in the UK, now has an increased global remit and will have responsibility for leading the development of work for government and the public sector worldwide.
Page joined Mori in 1987 and has been named as one of the "100 most influential people in the public sector" by the Guardian.
Page said: "Ipsos are already undertaking research on pan-global public sector projects in Singapore, Australia, America, Germany and France and I will be leading on the co-ordination of this major growth area."
Gosschalk said: "I am confident that Ipsos Mori will go from strength to strength under Mike and the strong senior team we now have in place."