Hayden, who joined the Magpies from Arsenal in 2016, has committed his future to the Magpies after the midfielder agreed a new six-year deal.
Darlow, who made the switch from Nottingham Forest to Tyneside in the summer of 2014, has penned a five-year deal with the club.
Hayden said: "I'm delighted. It shows a lot of loyalty and commitment from both sides.
"It's great to have agreed this before the start of the season and we can focus on getting the football right and getting as high up the Premier League table as we can."
Darlow, who made his Premier League debut away at West Bromwich Albion in 2015, was another key member of the Championship title-winning side after keeping 13 clean sheets in 34 league appearances.
Darlow said: "I'm really happy to have extended my stay. I've had five very good years and things are very positive here, especially with the new players coming in.
"There's a buzz around the place and that's great going into a new season. I'm happy to get sorted and give myself something to really get my teeth into."
Steve Bruce added: "I've been impressed with Karl. He hasn't played a lot because of the performances of Martin Dúbravka, but he's a very, very good goalkeeper and I'm delighted to tie him up.
"I'm delighted with Isaac too. He's a 25-year-old midfielder with his best years ahead of him.
"I know it has been a little bit on-off in terms of his future, so I'm very pleased he has committed himself to the club.
"We have had a very good week and a very good window with the players we have brought in, but the business we have done in terms of keeping players here has been very important too."
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