Korek, who is currently executive director of Frieze Los Angeles, will move to the UK capital to take up the position in March 2020.
She succeeds Peel, who resigned in June after three years in the job, citing "toxic personal attacks".
Korek to lead anniversary events
As incoming CEO, Korek will work alongside the gallery's creative director, Hans Ulrich Obrist, to lead a programme of events that celebrate the Serpentine's 50th anniversary next year.
"This is the only opportunity that could inspire me to leave Los Angeles," said Korek.
"Some of the most compelling qualities of LA as a city are embodied by the Serpentine as an institution: intrepid innovation, fluidity across disciplines, an irrepressible preoccupation with the future," she continued.
"I am thrilled to begin this endeavour and to continue to cultivate creative and philanthropic synergy between London, the US and the rest of the world."
Korek founded ForYourArt initiative
Korek has more than 15 years experience in the arts. Prior to her role as the inaugural executive director of Frieze Los Angeles, which launched in February this year, she founded and ran the ForYourArt initiative.
Founded in 2006, ForYourArt helps artists get their projects off the ground, and provides a weekly briefing on local events and exhibitions in Los Angeles. Its stated mission is to "expand art's place in everyday life".
Korek studied at Princeton University and began her career working at the Los Angeles County Museum of Art. She served on the Los Angeles County Arts Commission for eight years, and was its president from 2016 to 2017.
"Bettina Korek has a visionary understanding of art and its contexts and an incredible track record in supporting artists and their communities," said Obrist.
"I have come to appreciate her strategic acumen first-hand through frequent projects undertaken together in Los Angeles, where she has been a singular force in evolving a culture of civic engagement and patronage."
Serpentine has been operating without CEO
Obrist and chief operating and financial officer Monica Varriale have together been filling the interim role of CEO since Peel's resignation.
Peel resigned on the day that this year's Serpentine Pavilion by Junya Ishigami was unveiled, following criticism of Israeli cybertech firm NSO Group Technologies by human rights group Amnesty International.
NSO Group Technologies is largely owned by the regulated Novalpina Capital investment fund, which is managed by Peel's husband and others.
Peel warned that the attacks made against her risked eroding private philanthropic support of the arts, which she said would be "a great loss to everybody".
The Serpentine Galleries said in a statement at the time that it accepted Peel's resignation "with a mixture of gratitude and regret" and went on to praise her "immeasurable contribution" to the art world.
Updated February 2020
Following a legal complaint, the Guardian removed its article of 14 June 2019 and apologised to Mrs Peel. We are happy to clarify that Yana Peel is not, and was not, personally involved in the operation or decisions of the regulated Novalpina Capital investment fund, which is managed by her husband Stephen Peel, and others. Mrs Peel was not involved in any decision-making relating to the fund’s acquisition of NSO. Mrs Peel only has a small, indirect and passive interest in the fund. She does not own, whether directly or indirectly, any Novalpina Capital entity.