Satellite Edge Computing has been recently introduced to deploy innovative computational services in space using Low Earth Orbit (LEO) satellite constellations as a distributed computational platform. Running a distributed computing platform in space introduces new challenges to traditional problems like computation offloading, task scheduling, mobility management, fault detection, and recovery. This research focuses on the problem of task scheduling, proposing a system model that accounts for the dynamics of the Satellite Edge Computing environment and a formulation of the scheduling problem as an optimization problem that minimizes the average task response time under constraints on available resources and task completion deadlines. Then, we propose a decentralized algorithm that estimates the task response time and computes a scheduling solution in a fixed time, which depends only on the number of Inter Satellite Links a satellite has (typically four). Finally, we estimate and compare the overhead of the decentralized versus the decentralized solutions, showing the advantages of the proposed approach. Simulation experiments allow us to compare the performance of the decentralized approach with the performance of baseline decentralized and centralized solutions. Results show that, in all scenarios considered, the proposed decentralized algorithm performs better than the baseline centralized and decentralized solutions and is more scalable and highly available. © 2024 IEEE.