The former Stoke City boss, who entered a short-term agreement with the Saints in March, was rewarded for keeping them in the Premier League with a new three-year deal.
"Mark, Eddie and I are thrilled to have signed long-term contracts with the club. It was the only option we considered, having spent the last eight weeks with the club," the Welshman told the club's official website.
"Now it is vital that we take the unbelievable support we received from the fans during the last few games into next season. The staff and the players will work hard every day to deliver the success this club deserves, and with everyone pulling together we will achieve our goals."
Southampton ended the 2017-18 campaign in 17th place in the table, three points above the dropzone, having battled relegation for much of the campaign.