The 24-year joined Orient earlier this month on an initial 28-day deal.
He has made four appearances for Russell Slade's side, including a start in Tuesday's extra-time defeat to Hull City in the League Cup.
Slade told the club's official website: "We are delighted to keep Marvin on board, particularly as at one stage it looked like we might be losing him.
"He had a difficult start with us as he wasn't fully fit due to the injury he picked up at Burnley in pre-season.
"However, in training and during the limited minutes that he's had on the pitch, he's shown himself to be a very capable player. Trust me, there's a lot more to come."
Orient, who have won all four of their games in League One this season, scoring 11 goals in the process, visit Colchester United this afternoon.