Managing director Lee Charnley said: "Ryan and Jonas have both contributed significantly to Newcastle United over a number of years and on behalf of the board, I would like to place on record our sincere thanks to both players for the excellent service they have given the Club.
"It was a great pleasure to see Ryan and Jonas come back into the team in recent weeks and compete at the highest level after the injury and illness battles they have had to overcome.
"To come through those difficult periods with such strength and dignity will have given hope and inspiration to many and it is clear that our supporters have a deep connection and affection for both players, as does everyone associated with the Club."
Gutierrez joined the Magpies in July 2008 and in seven seasons on Tyneside made 205 appearances for United, scoring 12 goals.
His performances at the end of this season contributed significantly to Newcastle's survival in the Premier League and that special goal in the final game against West Ham, and the reaction of everyone present, is something all United supporters will remember.
Taylor overcame two knee ligament injuries to return to action. He made 110 appearances for the Club, hitting ten goals, and will be best remembered for his free-kick winner at the Stadium of Light in August 2011.