The 24-year-old centre back made 40 appearances for Blackpool last season.
The Scotsman began his career at hometown club Aberdeen and he has also represented Scotland up to Under-21 level.
“I think it’s the right step in my career to come here,” said Robertson.
“The last two years have probably been the best football I’ve played in my career so far and I think coming here is the right fit for me at the right time.
“Hopefully I can come here and play well and develop. I had other offers in League One but I think I’ve got to test myself in the Championship and I feel as though I’m ready to do that.”
The Millers have also signed Kyle Vassell from Blackpool. The 25-year-old striker scored 13 goals last season.