The new contract will see Milligan remain at Irongate until the end of the 2023/24 season.
Club chairman Brian Ginty said: "I am delighted 'Milly' has decided to commit to Brig.
"After an excellent start to the season, he has been attracting the attention of quite a few other clubs, including some higher up the pyramid; so getting his long-term commitment is superb news for us a club."
On the new deal, Milligan added: "I’m made up the club have offered me a contract as I have a really good relationship with the club and fans going back to my playing days. It’s great to be rewarded for all the hard work I’ve put in, but I couldn’t have done it without the hard work from the players and my staff.
"I have aspirations to manage higher but I’ve not done enough yet to even think about that. I’m still really early on in my managerial career.
"My main aim is to take this young team as high as they can go collectively and individually. I feel the way I want the players to play helps the younger boys to express themselves and enjoy training and playing.
"I love coaching this group as they give me everything and play exciting football which I love to watch and if we just keep working hard let’s see where it takes us."
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