Williams trained with the Shrimps over the summer and appeared to have secured a contract in October, only for international clearance issues to scupper the deal.
But the former Rhyl and Chester midfielder has now been given the green light to officially join up with Jim Bentley's squad and he will be available for selection this weekend at Plymouth Argyle in League Two.
Shrimps' boss Bentley told the club's official website: "I'm just glad it has all been done now and Ryan can continue his career.
"It has been a frustrating time for him and I am glad everything has been sorted."
