Brown, who has found a new lease of life under Brendan Rodgers, has signed a new two-year deal that will see him stay with the club until at least 2019. He has been increasingly influential in the middle of midfield and has returned to the international stage.
Meanwhile, Simunovic, who signed from Dinamo Zagreb in 2015, has penned a new four-year deal until at least the summer of 2021.
The centre-back appeared on his way out of the club last summer but stayed and emerged as the bedrock of the Celtic defence. He switched his allegiance from Croatia to Bosnia and Herzegovina this summer.