The club captain signed a new 12 month contract this week.
Dyche said: “From the day I became Everton manager, Seamus has been a great example to his teammates and staff on what it means to play for the Club.
“He is a model professional and helps set standards, and his leadership is rightly admired by everyone.
“His vast experience and know-how on the pitch will continue to be valuable qualities for us in the season ahead.”
Everton Director of Football, Kevin Thelwell, also told the club's website: “Everyone knows what Everton means to Seamus and, in turn, what Seamus means to Evertonians so we are delighted he has decided to be part of what will be a momentous last season at Goodison Park for the Club.
“Seamus is rightly held in high esteem across football for the leader and person he is. His experience and influence will continue to prove invaluable to Sean, his coaching staff and our squad both on and off the pitch.”