"Maximum day of sadness for the Albirroja (La Plata) family, our gladiator Jose Luis Brown has left. But his memory and love of the club will never depart," the club tweeted.
Known to his friends as Tata, Brown made 36 appearances for Argentina and scored the first goal in their 3-2 World Cup final victory over West Germany in 1986.
"Without Jose Luis Brown, we would never have won the World Cup in 1986. Tou never complained about a thing, Tata" Argentina legend Diego Maradona said on Instagram.
After a playing career that included stints in Spain and France, Brown was coach, along with Sergio Batista, of the national Under-23 squad which won the 2008 Olympics and fielded Lionel Messi, Juan Roan Riquelme and Sergio Agüero.