The 36-year-old leg-spinner played in 271 one-day internationals after making his debut in April 1990 and took 337 wickets - seventh in the all-time list.
India's highest wicket-taker in Test and one-dayers, Kumble is expected to return from the West Indies in the early hours of Thursday after the team's first-round exit from the World Cup.
Local media reported that the spinner has informed his team mates of his impending decision and would make his announcement in his hometown Bangalore.
The fourth highest wicket-taker in Test history, Kumble had said prior to the departure to the Caribbean that he would quit one-dayers on his return.
Kumble had played sporadically in the shorter version after the 2003 edition in South Africa, where India finished runners-up to Australia, before being recalled for the Caribbean event.
Nicknamed 'Jumbo', the Karnataka spinner played against Bermuda in what was India's only victory from three group matches in the World Cup.
In one-dayers, Kumble took four or more wickets in an innings on eight occasions with his best bowling analysis being six for 12 off 6.1 overs against the West Indies in Kolkata in Nov. 1993.
Kumble has four Test fifties to his credit, but did not quite prove his usefulness with the bat in one-dayers, finishing with a tally of just 938 runs.
A match-winner in Tests, especially at home, he will forever be remembered for taking all 10 wickets in a Test innings - only the second bowler after England's Jim Laker - against Pakistan in New Delhi in 1999.