The 30-year-old was the team-mate of arch rival Mohun Bagan's Sony Norde currently playing in the Indian Super League (ISL) for Mumbai City FC at Bangladesh club Sheikh Jamal.
Anselme has previously represented San Cristobal FC in the Dominican Republic and Aigle Noir AC in Haiti.
"Wedson is here (at the club tent) and has signed for us. We are happy to have him with us," a club official told IANS.
There were talks between the player and East Bengal for the last five months. Anselme finally signed on Tuesday, igniting their fans' excitement.
Coach Trevor Morgan will now hope that Anselme will fill up the void left by Nigerian striker Ranti Martins, who now plays for Penang FA in the Malaysian Super League.
But the club is yet to finalise the four foreigners list stipulated in the I-League with English defender Calum Angus and South Korean Do Dong-hyun's fate hanging in the balance.
The I-League starts on January 7 next year.