"Lewis will replace Schumacher, who over the past three years has made a significant contribution" to the constructor, the firm said in a statement, describing the appointment as a "new chapter" for the team.
Schumacher said had enjoyed his three years at Mercedes, although he accepted that results had been disappointing.
"I wish Lewis well and for the team to achieve the success we worked so hard for in the build-up," he said in the statement. I would like to thank the team for their trust and all the guys for their unconditional commitment.
"I will now concentrate on the next races."
Hamilton will drive alongside Nico Rosberg, who will be in his fourth year at Mercedes and won his first Formula One race this year in China. He described his move as a "fresh challenge".
"Together, we can grow and rise to this new challenge. I believe that I can help steer the Silver Arrows to the top and achieve our joint ambitions of winning the world championships," he added.
Mercedes team principal Ross Brawn paid tribute to Schumacher's dedication and enthusiasm for the sport but said he was thrilled to have secured the services of Hamilton.
"I believe that the combination of Lewis and Nico will be the most dynamic and exciting pairing on the grid next year and I am looking forward to what we can achieve together," he added.