Clarke, who found the net 11 times in 15 games for Scunthorpe at the start of the season, has made his loan move from Charlton permanent.
The news follows David McGoldrick was recalled by Nottingham Forest and loaned out to Championship side Ipswich.
Coventry boss Mark Robins was delighted to have signed a proven goalscorer.
"We knew it would be difficult to keep hold of David McGoldrick, so we've acted quickly," he said.
"We wanted to bring someone in that can score goals at this level and Leon can do that, as he has proven."