Belencoso, 34, started playing as a senior with amateurs Deportivo Rayo Cantabria. From 2002 to 2008, following a brief spell in Portugal, he competed mainly in Segunda División B, representing in that level Real Jaén, Mérida UD, CE L'Hospitalet.
He had been one of the most consistent performers and had been nominated as AFC Foreign Player of the Year.
The Spaniard reached Segunda División for the first time in the 2008-09 seasons, signing with local Castile-La Mancha club Albacete Balompié.
He made his debut in the competition on 31 August 2008, coming in as a late substitute in a 2-1 home win against Sevilla Atlético, but only scored twice in the league over the course of two full seasons.
Speaking about the new signing, manager Jose Molina said: "On behalf of the team management we welcome Belencoso to Atlético de Kolkata which will help us in further developing the nucleus of the team this year. My association with his style of football goes back to the Kitchee FC days in Hong Kong.
"He had been one of the most consistent performers and had been nominated as AFC Foreign Player of the Year. With Postiga and now Belencoso, I feel the need for the right strikers has been precisely addressed."