Jenkins, who has been at the SIB for five years, raised £17,000 for the air ambulance earlier this year in an unsuccessful attempt to complete the Marathon des Sables, a 156-mile ultra marathon across the desert on the edge of the Sahara.
Before joining the SIB, which provides loans, grants and strategic support to charities and social enterprises, Jenkins, a former merchant banker, was director of ventures at the social enterprise development charity UnLtd.
Jenkins, who will take up the new role in April, said: "I have followed the extraordinary progress of London’s Air Ambulance over the past few years as it became one of the capital’s most iconic charitable brands.
"The charity has already achieved so much, but I am excited to push it even further. I look forward to working alongside both the fundraising and operational teams to take this inspirational charity to new heights."
Mark Vickers, chair of London’s Air Ambulance, said: "With Jonathan at the helm, our charity is in a strong position to build on the momentum of our existing success. We look forward to seeing Jonathan use his impressive talents to act as an inspirational leader, a key spokesperson and a passionate advocate for our organisation, generating strong and long-lasting relationships with various stakeholders."