The 37-year-old left-hander reached the landmark during the third match against England in Hambantota when he took a single off Chris Woakes to move to 13.
Sangakkara lies behind three retired batsmen in the all-time list led by Sachin Tendulkar of India, who made 18,426 runs in 463 ODI matches.
Former Australian captain Ricky Ponting has 13,704 runs in 375 ODI matches and Sanath Jayasuriya of Sri Lanka has 13,430 runs in 445 games.
Sangakkara, who made his international debut in 2000, is also just 12 runs short of completing 12,000 Test runs. He has made 11,988 runs in 128 Tests. – AFP