Patterson, brought to the club by previous manager Andy Scott, led the Millers to four victories from his five games in charge as caretaker before the appointment of Evans on Monday.
Chief operating officer Paul Douglas said: "Everybody at the club would like to thank Darren for his commitment to the club and the excellent job he did, not only as assistant manager, but also after stepping in to take charge of the team.
"As well as having a very professional approach to his role at the club, Darren was a very approachable character and an amiable person to have around. Everyone at Rotherham United would like to wish him well for the future."
Paul Raynor has been appointed as Evans' new assistant, while chief scout Andy Harris has also left the club.
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