Thirty-three members of the council voted in favor of the draft contract, four were against and seven abstained.
Under the contract, the complex including an UEFA-standard football stadium, sports fields and other facilities will be built by Axis industries, which is part of the Icor Group, and managed and operated by Kauno Arena for more than two decades.
The complex will be designed by British architect Damon Lavelle of Populous, a global firm designing UEFA stadiums, and Lithuania's Cloud Architektai.
Vilnius Mayor Remigijus Simasius expects the contract to be signed next February.
According to the mayor, the demolition of the old structural skeleton of the stadium would begin soon, with a new structure planned to be built in 2023.
The construction of the stadium with 15,000 seats and a hybrid pitch and other facilities is estimated to cost around 93.2 million euros. However, if Vilnius' authorities opt to spread out the payments over 25 years, BaltCap, the largest private equity fund manager in the Baltic states, will receive a total of almost 156 million euros.
Under the current plan, the central government's share of project funding would amount to around 54.5 million euros, and Vilnius Municipality would provide 101.5 million euros. The government and the city would have the option of paying off earlier.
In addition to the football stadium, the complex will include an athletics stadium, a sports complex with gymnastics, handball, volleyball, boxing and basketball courts, a community and cultural education center with a library, a kindergarten, and a sports museum.