The 28-year-old Frenchman is well known to Shrimps’ boss Stephen Robinson after the latter’s short spell at Oldham Athletic in 2016.
Having originally come to England to play for Kidderminster Harriers, Fane spent three years at Boundary Park before being released at the end of the 2018/19 campaign.
A month-long spell at Shrewsbury Town followed before his contract was cancelled for personal reasons, enabling a return to France to be closer to his family.
The deal was announced an hour-and-a-half after Callum Jones’ recall by Hull City was made public.
Robinson said: “Ousmane gives us something different to the other midfielders that we have got at the club.
“He is very direct, breaks up the play and provides that extra bit of cover for the back four.
“I have worked with him before when I was the manager at Oldham. He’s got experience at League One level and I am delighted to get him into the building.”
Fane added: “I am very happy, I am very excited about this new challenge. I have been in England before and this is a new start again for me.
“I know the league well, I have played a lot of games in this league with Oldham.
“It is good to be back with the manager. We know each other from our time there and I really hope that we can work well together again.
“I am very energetic in midfield, I love to run, I love to do the dirty work for my team-mates.
“I will give my best every game, 100 per cent. I hope they will see that when I am on the pitch.”
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