Former Blackpool and Fleetwood Town pair take charge of non-league side Bamber Bridge
Milligan has been named first-team manager at the Sir Tom Finney Stadium following the departure of Joey Collins last week.
Hills, who has recently been in interim charge of AFC Fylde alongside Brett Ormerod, will take on the role of assistant manager.
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Hide AdMilligan, who spent a number of seasons with Brig as a player, was also recently part of former manager Neil Reynolds' coaching setup.
The 39-year-old helped the club win promotion to the NPL Premier Division in 2017 and scored the opening goal in their 2-1 victory over Grantham Town in the League Cup final that same year.
A former Blackpool and Fleetwood player, Milligan has recently appeared for AFC Blackpool in the North West Counties League.
Brig have been without a manager after Collins quit due to personal reasons following last week's 5-1 win over Wythenshawe Amateurs in the LFA Challenge Trophy.
The new management team will take charge of their first game this Saturday when Brig face a trip to Whitby Town.