Using fully kinetic simulations, we demonstrate that magnetic reconnection in relativistic plasmas is highly efficient at accelerating particles through a first-order Fermi process resulting from the curvature drift of particles in the direction of the electric field induced by the relativistic flows. This mechanism gives rise to the formation of hard power-law spectra in parameter regimes where the energy density in the reconnecting field exceeds the rest mass energy density σ ≡ B 2 /(4πnmec 2 ) > 1 and when the system size is sufficiently large. In the limit σ 1, the spectral index approaches p = 1 and most of the available energy is converted into non-thermal particles. A simple analytic model is proposed which explains these key features and predicts a general condition under which hard power-law spectra will be generated from magnetic reconnection.PACS numbers: 52.27. Ny, 52.35.Vd, 98.54.Cm, 98.70.Rz Introduction -Magnetic reconnection is a fundamental plasma process that allows rapid changes of magnetic field topology and the conversion of magnetic energy into plasma kinetic energy. It has been extensively discussed in solar flares, Earth's magnetosphere, and laboratory applications. However, magnetic reconnection remains poorly understood in high-energy astrophysical systems [1]. Magnetic reconnection has been suggested as a mechanism for producing high-energy emissions from pulsar wind nebula, gamma-ray bursts, and jets from active galactic nuclei [2][3][4][5][6]. In those systems, it is often expected that the magnetization parameter σ ≡ B 2 /(4πnmc 2 ) exceeds unity. Most previous kinetic studies focused on the non-relativistic regime σ < 1 and reported several acceleration mechanisms such as acceleration at X-line regions [7][8][9] and Fermi-type acceleration within magnetic islands [8][9][10][11]. More recently, the regime σ = 1-100 has been explored using pressure-balanced current sheets and strong particle acceleration has been found in both diffusion regions [12][13][14][15] and island regions [16,17]. However, this initial condition requires a hot plasma component inside the current sheet to maintain force balance, which may not be justified for high-σ plasmas.