The 31-year-old, who passed a medical on Friday morning, replaces Danny Ward who was recalled by injury-hit Liverpool on Monday.
Collin could go straight into the squad for the Premiership match against Ross County at the Global Energy Stadium this Sunday.
Manager Derek McInnes said: "We're still waiting for international clearance for Adam and I'll announce the team on Sunday morning. We had assurances from Liverpool that Danny could stay, but their circumstances changed, so we're delighted to get Adam on board."
Lee Camp arrived at the New York Stadium from Bournemouth over the summer and Collin struggled to oust him from Rotherham's starting XI, his last appearance coming on August 29.
"I'm excited at the prospect of joining a club of Aberdeen's size. It's a great opportunity," Collin told the Evening Express.
"Aberdeen are one of the biggest clubs in Scotland with a great history. I spoke to the manager Derek McInnes and can't wait to work with him. I should be fit and available for Sunday."
Source: Sky Sports