Prolific forward Brown joined the Baggies as a schoolboy and played for them between 1961 and 1981. His 279 goals and 720 appearances are both club records.
He was also part of the side that won the 1966 League Cup and the 1968 FA Cup; Albion's last pieces of major silverware.
"When the chairman called me two years ago to tell me his plans, I was dumbfounded," Brown said.
"When you go to away games, every now and again you see statues of players. But to know there is now going to be one of me at The Hawthorns is actually a funny feeling - but a special one."
Chairman Jeremy Peace said: "Tony is a West Bromwich Albion legend and it is only fitting that his immense contribution to the club will be celebrated in this way.
“He holds just about every club record there is and is one of the greatest players in our history.
“Of course, the most important factor in this process was Tony, and ensuring he was happy with the statue."