The Scottish champions endured a topsy-turvy start to the season domestically and in Europe, but a recent return to form sees the Glasgow club sat top of the Scottish Premiership and a comfortable second in UEFA Europa League Group D.
And a further boost has arrived at manager Ronny Deila's feet with skipper Brown committing his next three and a half years to Celtic.
He told the club's official website: "It's an absolute privilege to extend my contract with Celtic, a brilliant football club and with such incredible supporters.
"This is a place that I call home.
"Being Celtic captain is a tremendous honour and it is a role which I cherish dearly.
"The team is in a great place just now and we're all right behind the manager and the backroom team as they build for the future.
"I will do all I can with the manager and all the players at the club to deliver the success which our supporters deserve."
