The duo were presented with the Howard Kendall Award at the Club's End of season awards presentation which took place at the Philharmonic Hall on Tuesday night.
"We know how much of an exciting time it is for the Club," said Jagielka. "While we are in the latter stages of our careers, we are still delighted to be here and playing a part on and off the pitch.
"When we joined a great club like Everton, we hoped we would be part of the furniture and that seems to be the case.
"It's fantastic we both got this award together because we have enjoyed the ups and the downs alongside each other."
Baines added: "The award is a real nice acknowledgment for the time we have spent here.
"We have both played a lot of football in a lot of games and we have given everything we have had. Throughout our careers, we have given our best years to Everton and hopefully there is still a bit more left in us left. We want to continue to serve the Club well."