Gladness appeared in eight games with the NBA champion Heat last season, scoring two points and grabbing 11 rebounds before becoming a free agent after his second 10-day contract with Miami expired.
He finished the season by playing in 18 more games with Golden State, averaging 3.0 points and 2.6 rebounds.
Varnado was a second-round draft pick by Miami in 2010. He has played overseas since. Both Varnado and Gladness were on Miami's summer league roster in July.
Miami's roster stands at 15. The Heat can bring up to 20 players to training camp, which starts in late September.