The Irishman has struggled for opportunities since arriving at the Millers from Shamrock Rovers in the summer of 2019 and has now been allowed to move on, with injuries having not helped his cause.
Clarke, a one-time academy player at Middlesbrough, had a year left on his Millers deal.
Injury deprived him from making an early impact at the AESSEAL New York Stadium in 2019-20 - having suffered a knee injury in a behind-closed doors match shortly after joining.
Clarke, who can operate at left-back or in midfield, made his debut in the EFL Trophy game against Doncaster Rovers in October, scoring the winner. But the 23--year-old Dubliner failed to make himself a first-team regular.
The former Republic of Ireland Under 19 international, made eight league starts in his first season with the Millers and started nine Championship games last term.