Previous attempts by officials in 2004 and 2007 to redevelop the city-owned site fell through before construction ever started. Plans for high-rise condominium buildings stalled in part because developers weren't able to sell enough units in order to begin work.
The tower was selected from among five proposals made by developers to the city, which has agreed to contribute nearly $18 million from property taxes generated by the project.
The one- and two-bedroom apartments in the tower are to have floor-to-ceiling windows and balconies, with rents expected to range from $1,300 to $2,400 a month. The tower would be about the same height as the nearby City-County Building and be among about the dozen tallest downtown buildings.
David Flaherty, the CEO of Flaherty & Collins Properties, said the tower's design will make a "bold statement" for the city.
"As you come into our city from the north, the south or the east, this is one of the main things that you'll see," he said.
Market Square Arena was the home of the NBA's Indiana Pacers for 25 years and was the site of Elvis Presley's final concert before his death in 1977. It was demolished in 2001 following the construction of Conseco Fieldhouse.