According to the report, Williams told Wannstedt of his decision on Friday afternoon after Wannstedt's repeated attempts to talk his star player out of it.
Williams reportedly was on his way to India to begin several months of travel.
The move isn't official until Williams files retirement papers with the NFL, and he said he would do that either Tuesday or Wednesday.
The Williams move is the latest — and by far most damaging — blow in an atrocious offseason.
Williams obviously was the most important player on the team, having compiled the two best rushing seasons in franchise history in his two years with the Dolphins.