The 23-year-old winger has joined for an undisclosed fee from the Shakers and has the option of a third year.
Worrall, who will join up with the Millers as they prepare for life in League One, had no doubt the New York Stadium is the place he wanted to be.
"I had the opportunity to join other clubs but before I had made up my mind I heard of Rotherham United's interest, and it didn't take long for me to sign," he said.
"I spoke with Joe Skarz who I know well from Bury, had a look around the stadium and knew that it was a great move for me.
"Looking around it was a lot different to what I am used to, I spent five years at Bury where there were many ups at the start but last season was a struggle.
"As soon as I spoke to Rotherham and learned about what [manager] Steve Evans had planned I jumped at the chance to sign."
Worrall becomes the Millers' fourth signing of the summer following the captures of Joe Skarz, Richard Brindley and Adam Collin.
Evans, currently on holiday in Dubai, is keen on adding two more faces to his squad before they return to pre-season training next week.
"My squad will most likely take a further few weeks to be completed," he said. "I am hopeful another two or three further players will have joined us for when the lads report next Wednesday, and there is a couple that I want that may take a week or so longer."