The midfielder, who was offered the contract in February, has expressed his delight at securing another season at Elland Road.
Brown told the club's official website: "I'm delighted to sign the contract and get things sorted.
"The gaffer has made a lot of changes over the summer and I'm looking forward to being a part of things. There is a great team spirit here and everything has gone well in pre-season."
The 35-year-old has previously played under Leeds United manager Neil Warnock at Sheffield United.