Simms scored once in 12 Premier League appearances for the Toffees, including three starts.
He scored seven goals in 17 Sky Bet Championship games while on loan at Sunderland last season and has also spent time with Blackpool and Hearts.
The 22 year old will replace Sporting Lisbon-bound Viktor Gyokeres, who is set to join the Portuguese club for £22m.
Gyokeres finished as the Championship’s second top scorer last season with 21 goals and also provided 12 assists, the joint highest in the division.
Coventry missed out on promotion to the Premier League by the narrowest of margins last term, losing the play-off-final to Luton after a penalty shootout.
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