With Jordan and Andre Ayew at the African Nations Cup and Andre-Pierre Gignac injured, Deschamps was was running short of options in attack.
He told www.om.net: "It was vital for us in sport to have a more attacking player. Brandao is currently the only solution who is feasible financially and of interest to us from a sporting perspective.
"There is an economic situation that everyone knows about and we know what Brandao brought to the club before.
"He's a hard worker with good qualities. I know what he did for OM, he already knows the club and his team-mates."
Deschamps expects Brandao to be available to face Lille on Sunday.
Asked how long he might be with the team, Deschamps added: "We'll see. Do not ask me what will happen in several months, I'm here to manage in the short term, which is most important to us."
Brandao has scored 24 goals in 90 matches for Marseille. He was first loaned to Cruzeiro last March and, after failing to score in five games, moved on to Gremio in June.