Multi-area state estimation (MASE) is indispensable for coordination among independent system operators in interconnected systems. In this paper, we propose an adaptive distributed quasi-Newton (A-DQN) algorithm with an optimal step length tuning strategy for MASE in electric power systems. To address the nonlinearity of the measurement model, nonlinear MASE is factorized into two linear estimation stages with a nonlinear transformation in between. A-DQN is then applied to solve the two linear estimation stages in which the decomposed solution for optimal step length is derived in closed form by exploiting the problem structure. With this method, each area performs a local state estimation with limited information exchange with its neighbors; thus, no central coordinator is needed. Based on a peer-to-peer communication paradigm, this method provides accurate estimation results and considers coupling among areas while the privacy and independence of each area remain well-preserved. Numerical tests demonstrated that the proposed algorithm outperforms MASE methods based on state-of-the-art algorithms such as the alternating direction method of multipliers, the matrix-splitting-based distributed Newton method, and the existing distributed Broyden–Fletcher–Goldfarb–Shanno algorithm.