The Premier League's bottom club sacked Nathan Jones after just 95 days in charge earlier this month, having dismissed Ralph Hasenhuttl in November.
Selles' appointment comes after talks with former Leeds United manager Jesse Marsch broke down.
The Saints defeated Chelsea on Saturday in Spaniard Selles' one game as interim manager after Jones' sacking.
Prior to Saturday's victory over Chelsea, the 39-year-old confirmed he wanted to become the club's next permanent manager, saying he had been ready to become a "number one for the last four years".
Selles, who has coaching experience in Greece, Azerbaijan and Denmark, backed that up by helping his struggling side earn only their second league win since October.