Brosnan, who is Ireland's starting women's keeper, has signed a new two-year contract with Everton until the end of the 2026 season.
The 28-year-old is Everton's 2023/24 Players' Player of the Season.
Speaking about her new deal, Brosnan said, "I'm really excited to be continuing as an Everton player. I think everyone knows how much this club, the players, and the fans mean to me.
"To put on the Everton shirt is incredibly special. Having the opportunity to continue to do that was so important to me.
"I’ve really enjoyed my time here so far and I’ve created a lot of great memories with the girls and the fans, and hopefully that continues over the coming years."
Everton manager Brian Sorensen added, "I'm thrilled we're able to keep Courtney at the club.
"Without doubt, she is one of the best goalkeepers in this league and is highly regarded in our squad. She has continued to improve year-on-year and produced some unbelievable performances for us last season.
"As a person, Courtney is fantastic to work with. She’s exactly the kind of person we want as part of our group, and I’m really happy she feels settled here."
There's no place like home. 🏠@court_brosnan18 🔵 pic.twitter.com/o1i7I2YvBL
— Everton Women (@EvertonWomen) June 28, 2024
Ireland midfielder Ziu has also agreed to stay at West Ham.
The club has not disclosed the contract details but has said it is a "long-term deal."
The 22-year-old, who joined the Hammers from Shelbourne in 2022, spoke about her new deal and said being at West Ham was the only place she ever wanted to be.
"It feels amazing to have extended my contract at West Ham United," Ziu told West Ham TV.
"I love being here. From the moment I walked through the gates at Chadwell Heath, I knew this was where I wanted to be.
"Because of the knee injury that I sustained in my first year at the club, it feels like I'm only just getting started in a West Ham shirt. But I’m more determined than ever before, and I’m looking forward to coming back for pre-season and working hard to show what I can do in the seasons to come."
Eileen Gleeson names her Ireland squad for the French and England games next Wednesday. Both Ziu and Brosnan are expected to be part of that squad.
Locked in and ready for more! 🔒⚒️
— West Ham United Women (@westhamwomen) June 28, 2024