Jan 29 (Reuters) - Dublin-based online betting company Flutter said on Monday it will propose moving the primary listing of its shares from London to New York at the annual general meeting in May.

Subject to shareholders' approval, the transition to a U.S. primary listing is expected to become effective in late second quarter or early third quarter, Flutter said.

Flutter's New York Stock Exchange-listed shares are set to debut on Monday, while its secondary Dublin listing has been cancelled.

"We believe a US primary listing is the natural home for Flutter given Fanduel's #1 position in the US, a market which we expect to contribute the largest proportion of profits in the near future," CEO Peter Jackson said in a statement.

The company, home to Paddy Power, Betfair and Sportsbet brands, has been planning a U.S. listing since the start of last year after rapid growth in the business, which was the first to turn a profit since the lifting of a sports betting ban in the country in 2018. (Reporting by Eva Mathews in Bengaluru; Editing by Shounak Dasgupta and Shinjini Ganguli)