The 28-year-old is the Shrimps’ second signing of the week, following on from Tuesday’s arrival of Liam Gibson.
It is the third time Songo’o and Adams will have worked together following spells in Scotland and the South West.
Adams told the club website: “Yann is a central midfield player who I have managed twice before.
“I signed him for Ross County in the SPL on loan from Blackburn Rovers and then for Plymouth Argyle where he won promotion from League Two, playing over 120 games in three years for the club.”
Songo’o had spells in Spain, France and America before signing a two-year deal at Blackburn Rovers in August 2014.
The French-born midfielder who can also play in defence hails from a famous footballing family.
His dad, Jacques, is a former Cameroon international goalkeeper and his older brother, Franck, came through the ranks at Barcelona.
He also spent the majority of his youth career in Spain, playing for the likes of Deportivo La Coruna and Real Zaragoza, before having spells with Sabadell and Pobla de Mafumet.
He also enjoyed spells in America with MLS side Sporting Kansas City and Orlando City.
At international level, Songo’o represented Cameroon at the 2011 African Youth Championship in South Africa, helping his country reach the final and qualify for the 2011 FIFA Under-20 World Cup.