The exact dates for the tri-series, a prelude to the Champions Trophy tournament in India in October-November, will be announced later.
Each team will play the other twice in the league with the top two advancing to the final, Indian cricket board secretary Niranjan Shah said in a statement on Monday.
Three of the seven matches will be played in Singapore and the remaining four in the Malaysian capital of Kuala Lumpur, the statement said.
Singapore has previously hosted three tri-series, the first one in 1996 between India, Pakistan and Sri Lanka at Padang and two in 1999 and 2000 at the new Kallang ground.
Kuala Lumpur hosted one-day internationals when cricket was played at the Commonwealth Games in 2002.
The ground arrangements for the latest series will be organised by Cricket Australia (CA) while the Indian board will handle the marketing and sale of television rights, the statement added.
CA's chief executive James Sutherland said in Sydney he was grateful for the support of the Malaysian Cricket Association and the Singapore Cricket Association.
"It would be exciting to bring the game to newer cricketing frontiers and to showcase some of the best players in the world," Sutherland said.
The tournament would be Australia's first international series since it toured Bangladesh in April.
It would be the first step in what will be a huge season for Australia, including the Champions Trophy, the home Ashes series against England and the World Cup in the Caribbean, starting in March.