The club was founded after a businessman called Amadeu Horn gave football kits to a group of boys. The boys played a match against a team called Humaitá, and won. On September 1, 1923, at Amadeu Horn's house, the club was founded, known as Avahy Football Club at the time. The team was named Avahy after the Battle of Avay, in the Paraguayan War. In the following year, it became the first Santa Catarina State Championship champion.
Avaí has played in the Brazilian First Division ("Série A") eight times: 1974, 1976, 1977, 1979, 2009, 2010, 2011 and 2015. In 1998, they won their only national title, the Brazilian Third Division ("Série C"). From 1999 to 2008 and from 2012 to 2014, they played in the Série B with their best campaigns being the third place attained in 2004 (when Avaí reached the Final Four, but could not be promoted to the First Division because only the two best placed teams were promoted) and 2008.
In 2008 they finished 3rd in the championship and were promoted to the First Division for the first time in 30 years. In its first year playing in Série A, Avaí finished in 6th place, thus qualifying for the Copa Sudamericana. The team eventually was relegated in 2011, and returned to the Série A in 2014, when the team won the promotion in the last round. Avaí won the most Santa Catarina State Championship titles in the 20th Century (13), and is currently the all-time record state champions (16), just ahead of cross-bridge rivals Figueirense (15).
Avaí's stadium is Estádio Aderbal Ramos da Silva (though it's mostly referred to as Ressacada), and it was opened in 1983. It has a maximum capacity of 17,800 people, but its record crowd was 25,735 at the Catarinense Championship final. Before 1983, Avaí's stadium was Estádio Adolfo Konder (which has been subsequently demolished).