Veteran Gravesen, who spent five years at Goodison Park from 2000 to 2005, returned to the club on loan from Celtic last summer.

However, he has been limited to just 12 appearances this season due to injury and will now head back to Scotland.

Goalkeeper Wessels has started just two Premier League games for Everton since signing from Cologne on a one-year deal.

Wessels has been kept on the substitutes' bench by the form and fitness of first-choice keeper Tim Howard but he has impressed Moyes with his attitude.

"I would like to thank Stefan Wessels who will be leaving us," Moyes told the club's official website.

"His level of professionalism has been a credit to him and he has been a great man to have around the club.

"Thomas Gravesen will also depart following the completion of his season-long loan. He deserves thanks for both his spells here and we wish him well for the future."

Gravesen came on for the final five minutes of Everton's 3-1 win over Newcastle on Sunday, while Wessels was an unused substitute.