King was initially nominated as an interim successor to take over at the end of March, when Oswald is set to leave.
King has been at the FTSE 100-listed packaging group for 17 years in various strategy, business development and finance leadership roles.
“He has been instrumental in defining the group’s strategic direction since listing and I am confident he will bring significant insight and leadership to the role of CEO,” said chair David Williams.
“This appointment follows a formal review process, assessing both internal and external candidates, which convinced the board that he is the right person to lead the group.”
Shares dipped 1% to 1,642p on Tuesday morning.