The Hoops took out the Scottish Premier League title and the Scottish Cup this campaign and captain Brown is eager to back that up with more silverware next term and beyond.
"It's huge, not just for me, for every single player and the management staff as well, for everyone at Celtic," he said.
"It's a great club and the support we get week in, week out has been fantastic, so it's something to give back to them. We've got a great squad and hopefully we can keep the players.
"That's what we are trying to do. We have had a great season this year but we need to try and better it next season.
"We have three (Champions League) qualifiers coming up and we are back in quite early.
"Hopefully the squad can stay together but that's not up to me."