McGivern, who has been serving as the club's business director, succeeds Jim Kerr who stood down from the role earlier this month.
The 50-year-old Newtownabbey-based civil servant joined the Linfield board in May 2014.
"It will be a privilege to follow in the footsteps of some great men who have served this club with distinction through the years," said McGivern.
Kerr quit the chairman's position and his role as a director on 9 January.
Linfield have elected Roy McGivern as the club's new chairman.