Dobson, 26, will enter his sixth season at Craven Park next year, having joined the club midway through 2008, and takes over skipper duties from Galea, who has since signed for derby rivals Hull.
Centre Kris Welham, 25, has been named as vice-captain.
Head Coach Craig Sandercock said: “Michael captained the side early last season and did a really good job. He has great communication skills and is well respected by both the players and staff so it was a simple decision to appoint him as captain.
“As regards Kris, he has really started to show signs of being a good leader over the last 12 months. He is the classic case of someone who leads by example both on and off the pitch. Kris fully deserves to be our vice-captain and will develop even further as his career continues at Hull KR.”
Dobson burst on to the Super League scene as a teenager, during a loan spell at Catalan, where he scored 103 points in 12 appearances.
That attracted the attention of Wigan, who he helped survive relegation in 2006, before returning to the NRL with Canberra.
He came back to the UK in 2008, and has scored more than 1300 points in 126 games for Rovers since.
He said: “I’ve been here a few years now and enjoy having extra responsibility so it’s something I was more than happy to take on.
“It’s something I’m really looking forward to and intend to grab the role with both hands and enjoy it.”