Seltzer was 24-41 and had 14 players transfer from the program during his two seasons. Samford didn't say whether he was fired or resigned.
Padgett had been a Samford assistant since 2012 after stints with Manhattan College and the Wildcats.
The 37-year-old Padgett was a first-round NBA draft pick by the Utah Jazz in 1999, 28th overall. He played eight seasons with four teams.
The two-time All-Southeastern Conference forward helped the Wildcats win the 1998 national championship.
Padgett promised a pressing style of play similar to the systems he played in under Rick Pitino and Tubby Smith at Kentucky.