Miller worked with 27-year-old Brown at Craven Cottage, where the midfielder had loan spells at Brentford, TPS (Finland) and Bristol Rovers.
"Having known and worked with Wayne at Fulham FC for a number of years I am confident his physical and technical ability will be of great value to the squad," Miller said.
After leaving Fulham, Brown joined Bristol Rovers on a permanent basis before returning to Finland for another spell with TPS and then SJK.
"I worked under him (Miller) at Fulham and I know how professional, dedicated and passionate he is. This is the type of manager I want to work under that demands high standards and effort all the time," Brown said.
"I'm looking forward to pre-season, getting to know the rest of the team and learning how they play, hopefully I can fit in well.
"I'm looking forward to the challenge. The team has made progress this season and we will look to build and progress on and off the field next season.
"I'm looking forward to meeting the fans for the first time. I watched one of the derby games and the passion they showed was amazing and I can't wait to be part of that."
Brown, who made his Premier League debut for Fulham against Manchester United at Old Trafford in 2009, added: "I'm hoping to bring some goals and assistance to the club as part of the playing group. I like to shoot when I get the opportunity.
"I can play all across the midfield - I think my technical ability and passing range is my main asset that I can bring to the club."
