Obika, who started his career at Tottenham Hotspur has agreed a two-year contract with the Shrimps after leaving St Mirren.
The deal is subject to international clearance coming through.
During his time with Spurs, Obika had loan spells at seven clubs - Yeovil, Millwall, Crystal Palace, Peterborough, Swindon, Brighton and Charlton.
He left Spurs in 2014 to sign for Swindon, and has since played for Oxford United and recently St Mirren.
Obika said: "I am delighted to sign. I know the manager from his time at Motherwell and like the system he plays.
"There is a lot of freedom in there which I hope will suit my game.
"I started my career at Spurs and made a few first team appearances. I have had a lot of experience at League One and Championship level and have learned a lot over the years.
"I like to think of myself as a powerful player who is direct and likes to commit defenders and link play. I enjoy the whole heart of being a striker and am looking forward to the season starting.
"I'm coming into a side with a winning mentality after winning promotion last season and I am looking to add to that.'"
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