The 25-year-old Australian was set to join Second Division side Sheffield Wednesday on a short-term deal before Peter Taylor came in with a permanent offer.
Wednesday boss Chris Turner said: "It's good for the boy but unfortunate for ourselves that Hull City have offered him a three-year deal. In the current climate, you don't turn down that sort of offer for a trial spell."
Milosevic was signed for Leeds by David O'Leary in January 2000, leaving Australian side Perth Glory for the sum of £100,000. He hasn't made a first team appearance for Leeds, and played just once in a loan spell at Plymouth last year, and once for Crewe earlier this year. He has also been capped for his country at Under-23 level.
Meanwhile, City have turned down a bid from Doncaster Rovers for Andy Holt as he is now in Peter Taylor's first team plans.
Elsewhere, ex-Tiger Rob Matthews has re-signed for Mossley. The 32-year-old winger left City in 2002 after making 30 appearances in all competitions in just over a year at Boothferry Park. He joined Northwich Victoria before moving on to Mossley. He then had a brief spell at Altrincham but has now rejoined the North West Counties League side.