She said: "We face an enormous task with our goal of doubling native woodland cover, but we are fortunate in our dedicated staff."
Dr Nicholls has played a big part in the charity's partnership schemes and took a lead in its flagship acquisition in Hertfordshire, Heartwood Forest.
The former chemist worked in private equity for 18 years and currently splits time between the trust and other groups across business and education.
She said most of her time was dedicated to working towards the Woodland Trust's vision of "a country rich in native woods and trees, enjoyed by everyone".
Dr Nicholls, who replaces outgoing chair John Lake, said: "The trust has already achieved so much. I am excited to be working with the staff more closely in the months and years to come."