The move takes Button back to the team that gave him his Formula 1 debut in 2000, before he went on to become 2009 world champion and win 15 grands prix.
Button, 40, said Williams' role in his career and the "history and heritage" meant they were "close to my heart".
He said: "I am going to do my part to help the team back to the front. I can't wait to spend time with the drivers and the staff."
Williams were bought out by investment group Dorilton Capital last summer, and founder Sir Frank Williams and his family are no longer involved. The team are going through a restructuring aimed at reviving their fortunes after three seasons of finishing last in the championship.
New chief executive officer Jost Capito, who starts with the team next month, said: "Bringing Jenson back on board is another positive step to help us move forward as a team, both on and off track.