Kansas lost assistant Norm Roberts, a key recruiter for Self, on Tuesday when Roberts was hired to coach at St. John's.
Padgett, who started 19 of 31 games this season, created another off-season hit for the Jayhawks with his stunning news.
"Obviously we're all disappointed with David's decision," Self said. "Even though we don't agree with it, we're certainly respectful of it. We do wish him well with his future opportunities.
"We wish David and his family the best and we certainly appreciate the one year of effort he gave us here at Kansas."
Padgett was recruited to Kansas by former coach Roy Williams, who bolted for North Carolina. The 6-11 center, who averaged 6.5 points and 4.5 rebounds and led the Jayhawks with 43 blocked shots, was unhappy with how he was used by Self.