The England international, 33, penned a new deal with the Merseysiders on Monday.
"It's fantastic for everyone - the club, Steven and the fans," Ayre told Liverpool's official website. "He is - and always has been - such a big part of Liverpool Football Club.
"Particularly in this day and age, it's rather unique to find a local player who has given his whole career to his club."
Gerrard signed his first professional contract with Liverpool in 1998.