The 35-year-old midfielder -- capped 53 times -- has 609 Premier League games under his belt, only 23 shy of Welsh legend Giggs's mark, committed himself to the club until 2018.
"Let's hope (Barry) will smash every record. He's a quiet person but a strong character. He is 35 but he is still so important for the team," Everton manager Ronald Koeman told the club website.
Another England international, defender Leighton Baines, also put pen to paper to extend his present contract to 2019.
Baines, 32 and capped 30 times, is involved in his 10th campaign for Everton having signed from Wigan Athletic in 2007.
"The majority of my career I've spent here at Everton and it's something that I hope will continue even beyond these next few years," said Baines.
"I hope I'm always affiliated with Everton."
Koeman also persuaded a player at the other end of the age scale, 20-year-old defender Mason Holgate -- who made his senior debut this term -- to also extend his present deal to 2021.
"Mason is one of the big talents at the club," Koeman said.
"Of course, he started playing this season and did a great job. He's the future for the club and other young players like him."