济 is read jǐ in the river's name and in places named after it: 济南 'south of the Ji', 济宁 in Shandong and 济源 'source of the Ji' in Henan. Everywhere else, as in 经济 'economy' and 救济 'relief', it is jì.
history
The Four Rivers (四渎) of antiquity were the four that ran to the sea on their own: the Yangtze, the Yellow River, the Huai and the Ji. When the Yellow River broke its banks in 1855 and swung north, it took over the Ji's old channel to the sea.
